Yukiyasu Ozeki
| Department of Engineering Science | Professor |
| Cluster III (Fundamental Science and Engineering) | Professor |
- Profile:
Nonequilibrium Relaxation Method
Gauge Theory for Random Systems
Theory for Spin Glasses
Statistical Physics on Magnetizm
Theory for Superionic Conductors
Researcher Information
Research Keyword
Career
Educational Background
Research Activity Information
Paper
- Size-Independent Scaling Analysis for Percolation Systems
Yukiyasu Ozeki; Kenta Hagiwara
Statphys 28, T1-09A-06, Aug. 2023, Peer-reviwed
International conference proceedings, English - Critical Universality of 3D +/- J Ising Model Analyzed by the Dynamical Scaling Method
Yusuke Terasawa; Yukiyasu Ozeki
Statphys 28, Psa-65, Aug. 2023, Peer-reviwed
International conference proceedings, English - Dynamical Scaling Analysis and Estimation of Critical Exponent z for event-chain Algorithm
Yuma Osada; Yukiyasu Ozeki
Statphys 28, Psa-03, Aug. 2023, Peer-reviwed
International conference proceedings, English - Size-independent scaling analysis for explosive percolation
Kenta Hagiwara and Yukiyasu Ozeki
Corresponding, Physical Review E, American Physical Society, 106, 1, 054138, 15 Nov. 2022, Peer-reviwed, True
Scientific journal, English - Dynamical scaling analysis of symmetry breaking for the antiferromagnetic triangular Heisenberg model in a uniform field
Kazuaki Murayama; Yukiyasu Ozeki
Physical Review B, American Physical Society, 101, 9, 184427, 26 May 2020, Peer-reviwed
Scientific journal, English - Dynamical scaling analysis on critical universality class for fully frustrated XY models in two dimensions
Yukiyasu Ozeki; Yuri Yajima; Yuka Nakamura
Lead, PHYSICAL REVIEW B, AMER PHYSICAL SOC, 101, 9, Mar. 2020, Peer-reviwed, Critical properties of the fully frustrated XY models on square and triangular lattices are investigated by means of the nonequilibrium relaxation (NER) method. We examine the validity of the conclusion on the universality class of the chiral transition previously obtained by the NER method, in which that belongs to a non-Isingtype one. To clarify it, we analyze the NER of fluctuations for longer Monte Carlo steps on lager lattices than those performed previously. The calculation is made at the chiral transition temperatures estimated carefully by the use of recently improved dynamical scaling analysis. The result indicates that the asymptotic behavior of the time-dependent exponents, which should converge to the critical exponents, show the same tendency as those obtained previously in shorter times. We also apply the improved dynamical scaling analysis to the estimation of Kosterlitz-Thouless (KT) transitions and confirm the existence of the double transitions for the chiral and KT phases with more reliable estimations.
Scientific journal, English - Dynamical scaling analysis of phase transition and critical properties for the RP2 model in two dimensions
Yukiyasu Ozeki; Atsuyuki Matsuda; Yuki Echinaka
Physical Review E, American Physical Society, 99, 1, 012116, 11 Jan. 2019, Peer-reviwed
Scientific journal, English - Improved dynamical scaling analysis using the kernel method for nonequilibrium relaxation
Yuki Echinaka; Yukiyasu Ozeki
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 94, 4, 043312, Oct. 2016, Peer-reviwed, The dynamical scaling analysis for the Kosterlitz-Thouless transition in the nonequilibrium relaxation method is improved by the use of Bayesian statistics and the kernel method. This allows data to be fitted to a scaling function without using any parametric model function, which makes the results more reliable and reproducible and enables automatic and faster parameter estimation. Applying this method, the bootstrap method is introduced and a numerical discrimination for the transition type is proposed.
Scientific journal, English - Dynamical scaling in nonequilibrium relaxation analysis including corrections to scaling
Yukiyasu Ozeki
Statphys 26, p-1-44, Jul. 2016, Peer-reviwed
International conference proceedings, English - Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions
Yukiyasu Ozeki; Satoshi Yotsuyanagi; Takuya Sakai; Yuki Echinaka
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 89, 2, 022122, Feb. 2014, Peer-reviwed, The critical exponents are estimated for the gauge glass model in two dimensions, in which only the Kosterlitz-Thouless (KT) phase appears in the low-temperature regime. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents: the static exponent eta and the dynamical exponent z. Since the system exhibits criticality in the whole KT phase, we estimate the exponents on the boundary as well as inside the KT phase. The static exponent eta depends on both the temperature and the strength of randomness, while the dynamical one z is almost constant throughout the KT phase, including the boundary.
Scientific journal, English - Improved KT scaling for nonequilibrium relaxation analysis by the use of Bayesian inference and kernel method
Yukiyasu Ozeki; Yuki Echinaka
Statphys 25, pp1-2-22, Jul. 2013, Peer-reviwed
International conference proceedings, English - Nonequilibrium Relaxation Study of Effect of Randomness on Critical Universality Classes of Ferromagnetic Phase Transitions
Yukiyasu Ozeki; Satoshi Yotsuyanagi; Nobuyasu Ito
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 81, 7, 74602, Jul. 2012, Peer-reviwed, The ferromagnetic critical exponents are estimated along the phase boundary for the gauge glass model in three dimensions. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents. Together with the previously obtained results for the +/-J Ising model in two and three dimensions, universality classes are examined for these disordered models. The result reveals a direct numerical confirmation of the Harris criterion for typical models with positive, zero and negative values of alpha(0), the exponent for the specific heat in the regular case. In addition, we show a nonuniversal behavior of the dynamical exponent z with respect to the randomness for these models irrespective of alpha(0).
Scientific journal, English - Effects of randomness on critical exponents of Kosterlitz-Thouless transition in disordered XY models
Yukiyasu Ozeki; Takuya Sakai
Statphys 24, 234, Jul. 2010, Peer-reviwed
International conference proceedings, English - Nonequilibrium relaxation analysis for the spin glass transition in the +/-J Ising model in 3D
Yukiyasu Ozeki; Taichi Sugaya; Atsushi Hagiwara
Statphys 24, 241, Jul. 2010, Peer-reviwed
International conference proceedings, English - Nonequilibrium Relaxation Analysis for Universality in Kosterlitz-Thouless Transitions in Disordered Systems
Yukiyasu Ozeki; Takuya Sakai
Activity Report 2009, ISSP, 185, Jun. 2010
Research institution, English - NONEQUILIBRIUM RELAXATION STUDIES FOR FRUSTRATED SPIN SYSTEMS WITH KOSTERLITZ-THOULESS TRANSITIONS
Yukiyasu Ozeki; Satoshi Yotsuyanagi
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, WORLD SCIENTIFIC PUBL CO PTE LTD, 20, 9, 1367-1376, Sep. 2009, Peer-reviwed, The q-state clock gauge glass model in two dimensions with q = 6, 8, 10, 12, 14, 16 is studied by the use of the nonequilibrium relaxation analysis of the Kosterlitz-Thouless (KT) transition. The successive transitions of FM-KT-PM phases are investigated along the Nishimori line. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q(2). While the present model is not self-dual, we have a remarkable behavior with respect to the duality relation derived for the self-dual Villain-type model.
Scientific journal, English - Nonequilibrium Relaxation Study on Spin Glass Transition and Universality for the +/-J Ising Model
Yukiyasu Ozeki; Taichi Sugaya; Atsushi Hagiwara
Activity Report 2008, ISSP, 173, Jun. 2009
Research institution, English - Effects of discreteness on gauge glass models in two and three dimensions
Satoshi Yotsuyanagi; Yusuke Suemitsu; Yukiyasu Ozeki
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 79, 4, 041138, Apr. 2009, Peer-reviwed, The q-state clock gauge glass model is studied to see the effect of discreteness on the Kosterlitz-Thouless (KT) transition and the ferromagnetic (FM) critical phenomenon in random systems. The nonequilibrium relaxation analysis is applied. In two dimensions, the successive transitions of paramagnetic (PM), KT, and FM phases are investigated along the Nishimori line for q=6, 8, 10, 12, 14, 16, and 1024 (recognized as infinity) cases. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q(2). In three dimensions, the critical behavior of the PM-FM transition is studied along the Nishimori line for q=6, 8, 16, and 1024 cases. It is found that the spin discreteness is irrelevant, and the transition belongs to the same universality class as in the (continuous) XY case.
Scientific journal, English - Nonequilibrium Relaxation Analysis for Universality in Disordered Systems
Yukiyasu Ozeki; Satoshi Yotsuyanagi
Activity Report 2007, ISSP, 194, Jun. 2008
Research institution, English - Nonequilibrium relaxation method
Yukiyasu Ozeki; Nobuyasu Ito
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, IOP PUBLISHING LTD, 40, 31, R149-R203, Aug. 2007, Peer-reviwed, The nonequilibrium relaxation (NER) method is a numerical technique to analyse equilibrium phase transitions. One can estimate the transition point and critical exponents calculating relaxations of order parameter and fluctuations in NER processes from nonequilibrium initial states to the equilibrium ones. It is applied to the second-order transition as well as the first-order one; the precise estimation of transition temperature for the latter case is achieved with the mixed phase initialization technique. Since the equilibration is not necessary in the simulation, one can analyse systems with large sizes which can be recognized as in the thermodynamic limit up to the observation time. This leads to the analysis being more efficient for slowly relaxing systems with frustrations and randomness. It can be extended to the Kosterlitz-Thouless transition and the spin glass transition cases by the use of the finite-time scaling analysis. It is also extended to quantum systems.
Scientific journal, English - Nonequilibrium Relaxation Studies for Universality Classes and Random Fixed Point in Some Disordered Systems
Yukiyasu Ozeki
Statphys 23, 318, Jul. 2007, Peer-reviwed
International conference proceedings, English - Applications of Nonequilibrium Relaxation Method: Random Zq Models in Two and Three Dimensions
Yukiyasu Ozeki; Satoshi Yotsuyanagi
Activity Report 2006, ISSP, 198, Jun. 2007
Research institution, English - Application of Nonequilibrium Relaxation Method: Clock Gauge Glass Models in Two Dimensions
Yukiyasu Ozeki; Satoshi Yotsuyanagi
Activity Report 2005, ISSP, 219, Jun. 2006
Research institution, English - Gauge theory for quantum spin glasses
S Morita; Y Ozeki; H Nishimori
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 75, 1, 014001, Jan. 2006, Peer-reviwed, The gauge theory for random spin systems is extended to quantum spin glasses to derive a number of exact and/or rigorous results. The transverse Ising model and the quantum gauge glass are shown to be gauge invariant. For these models, an identity is proved that the expectation value of the gauge invariant operator in the ferromagnetic limit is equal to the one in the classical equilibrium state on the Nishimori line. As a result, a set of inequalities for the correlation function are proved, which restrict the location of the ordered phase. It is also proved that there is no long-range order in the two-dimensional quantum gauge glass in the ground state. The phase diagram for the quantum XY Mattis model is determined.
Scientific journal, English - Applications of Nonequilibrium Relaxation Method: XY Villain Model in Two Dimensions
Yukiyasu Ozeki; Nobuyasu Ito
Activity Report 2004, Issp, 178, Jun. 2005
Research institution, English - Nonequilibrium relaxation analysis of gauge glass models in two dimensions
Y Ozeki; K Ogawa
PHYSICAL REVIEW B, AMERICAN PHYSICAL SOC, 71, 22, 220407(R), Jun. 2005, Peer-reviwed, The Kosterlitz-Thouless (KT) transition is investigated for gauge glass models in two dimensions by means of the nonequilibrium relaxation (NER) method. Two kinds of models, which have the same symmetry, are analyzed. Using the scaling analysis of the NER function on a large lattice with L=1000, we confirm the KT transition numerically for both models. This indicates the stability of the KT phase against a small disorder, which was previously claimed by perturbation expansion and renormalization group arguments.
Scientific journal, English - Dynamical approach for gauge glass models
Y Ozeki
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE, 157, 157, 86-89, 2005, Peer-reviwed, The gauge glass models are investigated from dynamical points of view. First, the gauge theory is extended to dynamical systems with both stochastic and deterministic dynamics. Some exact dynamical relations are derived. This provides an argument for the absense of re-entrant transition, which is also derived by the static theory. Next, the nonequilibrium relaxation analysis is applied to 2D systems. From the relaxation of order parameter, we find a typical divergence of the relaxation time at finite temperature in disordered regime, which reveals the stability of the KT phase against a weak disorder.
Scientific journal, English - Nonequilibrium Relaxation Analysis for Gauge Glass Models in Two Dimensions
Yukiyasu Ozeki; Nobuyasu Ito
Activity Report 2003, ISSP, 194, Jun. 2004
Research institution, English - Critical exponents of isotropic-hexatic phase transition in the hard-disk system
H Watanabe; S Yukawa; Y Ozeki; N Ito
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 69, 4, 045103, Apr. 2004, Peer-reviwed, The hard-disk system is studied by observing the nonequilibrium relaxation behavior of a bond-orientational order parameter. The density dependence of characteristic relaxation time tau is estimated from the finite-time scaling analysis. The critical point between the fluid and the hexatic phase is refined to be 0.899(1) by assuming the divergence behavior of the Kosterlitz-Thouless transition. The value of the critical exponent eta is also studied by analyzing the fluctuation of the order parameter at the criticality and estimated as eta=0.25(2). These results are consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.
Scientific journal, English - Nonequilibrium relaxation analysis of fully frustrated XY models in two dimensions
Y Ozeki; N Ito
PHYSICAL REVIEW B, AMERICAN PHYSICAL SOC, 68, 5, 42-47, Aug. 2003, The nonequilibrium relaxation (NER) method is applied to the fully-frustrated XY models on square and triangular lattices. The transition temperatures of chiral and Kosterlitz-Thouless transitions are estimated with a high degree of precision on very large lattices. It is found that these two transitions occur at different temperatures for both models, which indicates the double transition and the existence of the intermediate phase. Further, we calculate the NER functions of fluctuations for chiral transition to estimate critical exponents. It is indicated that these models belong to the same universality class which is of different from the Ising class in two dimensions.
Scientific journal, English - Nonequilibrium relaxation analysis of fully frustrated XY models in two dimensions
Y Ozeki; N Ito
PHYSICAL REVIEW B, AMERICAN PHYSICAL SOC, 68, 5, 054414, Aug. 2003, Peer-reviwed, The nonequilibrium relaxation (NER) method is applied to the fully-frustrated XY models on square and triangular lattices. The transition temperatures of chiral and Kosterlitz-Thouless transitions are estimated with a high degree of precision on very large lattices. It is found that these two transitions occur at different temperatures for both models, which indicates the double transition and the existence of the intermediate phase. Further, we calculate the NER functions of fluctuations for chiral transition to estimate critical exponents. It is indicated that these models belong to the same universality class which is of different from the Ising class in two dimensions.
Scientific journal, English - Dynamical Rushbrooke's inequality for nonequilibrium relaxation process
Y Ozeki; N Ito
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 36, 19, 5175-5179, May 2003, Peer-reviwed, An inequality for dynamic critical exponents is proved for relaxation processes of arbitrary. magnetic systems. This is a dynamical extension of Rushbrooke's inequality. It can be applied to any continuous-transition systems with various dynamics. The relation is demonstrated on the result of nonequilibrium relaxation analysis. of fluctuations applied to the three-dimensional ferromagnetic Ising model.
Scientific journal, English - Nonequilibrium relaxation study on spin glass model
N Ito; Y Ozeki
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, 321, 1-2, 262-270, Apr. 2003, Peer-reviwed, Ferromagnetic (FM) transition point and universality class of the +/-J Ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation (NER) method. At FM bond density p between multicritical one p(me) and 1, static exponents take universal values which are different from those of p = 1 or p = p(me), and they are consistent with the values of the random-fixed point and of the simulations and experiment,, for diluted Ising systems. The dynamical exponent. however. seems to depend on p and not to be universal, although it may be due to finite-time correction. The estimation of p(me) on square lattice is also refined to be 0.8894(9). which is consistent with the Nishimori and Nemoto's conjecture. 0.889972 . . . (C) 2002 Elsevier Science B.V. All rights reserved.
Scientific journal, English - Nonequilibrium relaxation analysis for first-order phase transitions
Y Ozeki; K Kasono; N Ito; S Miyashita
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, 321, 1-2, 271-279, Apr. 2003, Peer-reviwed, The nonequilibrium relaxation method is applied to first-order transition systems. Using the mixed-phase initialization, one can avoid the influence of the meta-stable states and the hysteresis phenomenon in the simulation. The transition point is estimated accurately on very large lattices. To check the validity and efficiency of the method. we apply it to the ferromagnetic Potts model with q = 20 and 5 in two dimensions together with a demonstration of hysteresis phenomenon in the standard initializations. (C) 2002 Elsevier Science B.V. All rights reserved.
Scientific journal, English - Dynamical gauge theory for the XY gauge glass model
Y Ozeki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 36, 11, 2673-2693, Mar. 2003, Peer-reviwed, Dynamical systems of gauge glass are investigated by the method of gauge transformation. Both stochastic and deterministic dynamics are treated. Several exact relations are derived from dynamical quantities such as equilibrium and nonequilibrium auto-correlation functions, relaxation functions of order parameter and internal energy. They provide physical properties in terms of dynamics in the SG phase, a possible mixed phase and the Griffiths phase, the multicritical dynamics and the aging phenomenon. We also have a plausible argument for the absence of re-entrant transition in two or higher dimensions.
Scientific journal, English - Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition
Y Ozeki; K Ogawa; N Ito
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 67, 2, 026702, Feb. 2003, Peer-reviwed, A simple and efficient numerical analysis is proposed for the Kosterlitz-Thouless (KT) phase transition. The nonequilibrium relaxation method is applied to it. The two-dimensional ferromagnetic XY models are investigated to show the efficiency. At the KT transition point as well as inside the KT phase, the nonequilibrium relaxation of magnetization from the all-aligned state shows an asymptotic power-law decay, m(t)similar tot(-lambda(T)). Only outside the KT phase, an asymptotic single exponential decay is observed. Using a standard scaling form m(t)=tau(-lambda)(m) over bar (t/tau) in this regime, where tau is the relaxation time at each temperature, we find a simple and efficient numerical estimation of the KT transition point and dynamical exponent. This method can be applied to various kinds of models which show the KT-like behavior.
Scientific journal, English - Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition
Yukiyasu Ozeki; Keita Ogawa; Nobuyasu Ito
Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 67, 2, 5-196, 2003, A simple and efficient numerical analysis is proposed for the Kosterlitz-Thouless (KT) phase transition. The nonequilibrium relaxation method is applied to it. The two-dimensional ferromagnetic [Formula presented] models are investigated to show the efficiency. At the KT transition point as well as inside the KT phase, the nonequilibrium relaxation of magnetization from the all-aligned state shows an asymptotic power-law decay, [Formula presented] Only outside the KT phase, an asymptotic single exponential decay is observed. Using a standard scaling form [Formula presented] in this regime, where [Formula presented] is the relaxation time at each temperature, we find a simple and efficient numerical estimation of the KT transition point and dynamical exponent. This method can be applied to various kinds of models which show the KT-like behavior. © 2003 The American Physical Society.
Scientific journal, English - Nonequilibrium relaxation study on the ferromagnetic transition of Ising spin glass model
N Ito; Y Ozeki
COMPUTER SIMULATION STUDIES IN CONDENSED-MATTER PHYSICS XV, SPRINGER-VERLAG BERLIN, 90, 34-41, 2003, Ferromagnetic transition of the +/-J Ising model is studied simulationally for the cubic lattice. Nonequilibrium relaxation method is used to locate the transition point and to estimate the values of exponents. The dynamical exponent z increases smoothly when the density of ferromagnetic interaction, p, is decreased from 1. The static exponents are changed discontinuously when p is decreased from 1, and they stay in a universality class when p(mc) < p < 1, where p(mc) denotes the value of multicritical density. At p = p(mc), the static exponents are different from those in p(mc) < p < 1 and p = 1.
International conference proceedings, English - Numerical study of critical exponents for Kosterlitz-Thouless transition systems
Y Ozeki; N Ito
COMPUTER SIMULATION STUDIES IN CONDENSED-MATTER PHYSCIS XVI, SPRINGER-VERLAG BERLIN, 95, 106-112, 2003
International conference proceedings, English - Critical exponents of the two dimensional melting
H Watanabe; S Yukawa; Y Ozeki; N Ito
COMPUTER SIMULATION STUDIES IN CONDENSED-MATTER PHYSCIS XVI, SPRINGER-VERLAG BERLIN, 95, 101-105, 2003
International conference proceedings, English - Nonequilibrium relaxation analysis of two-dimensional melting
H Watanabe; S Yukawa; Y Ozeki; N Ito
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 66, 4, 041110, Oct. 2002, The phase diagram of a hard-disk system is studied by observing nonequilibrium relaxation functions of a bond-orientational order parameter using particle dynamics simulations. From a finite-time scaling analysis, two Kosterlitz-Thouless transitions can be observed when the density is increased from the isotropic fluid phase to closest packing. The transition densities are estimated to be 0.901(2) and 0.910(2), where the density denotes the fraction of area occupied by the particles, the density is normalized to one for the quadratic packing configuration. These observations are consistent with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory.
Scientific journal, English - Development and Applications of Nonequilibrium Relaxation Method
ISSP Computer Center Activity Report 2001, 189, 2002
English - Numerical evidence of infinite number of pure states near ferromagnetic phase boundary for short-range spin-glass systems
Y Ozeki; N Ito; K Ogawa
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 70, 12, 3471-3474, Dec. 2001, Numerical evidence that the number of pure states in the spin glass phase is infinite near the ferromagnetic phase. boundary for the three dimensional (3D) +/-J Ising model and 3D gauge glass models is presented. It is consistent with the mean field theory which suggests the multivalley structure of the spin glass phase. We will show that the onset of the ferromagnetic long-range order and that of the ferromagnetic spontaneous symmetry breaking do not coincide with each other, and this phenomenon characterizes the structure of the phase space.
Scientific journal, English - Nonequilibrium relaxation study of Ising spin glass models
Y Ozeki; N Ito
PHYSICAL REVIEW B, AMER PHYSICAL SOC, 64, 2, 024416, Jul. 2001, As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The +/-J Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of L=127 and for four-dimensional (hypercubic) lattice up to L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) Q(t,t(w))equivalent to[<S-i((1)) (t+t(w))S-i((2)) (t+t(w))>F], which is a spin correlation of two replicas produced after the waiting time t, from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development (t much greater thant(w)) in the SG phase. This provides a reliable upper bound of the transition temperature T-g. It is also found that a scaling relation Q(t,tw) = t(w)(-lambda) (q)(Q) over bar (t/t(w)), holds just around the transition point providing the lower bound of T-g. Together with these two bounds, we propose a new dynamical way for the estimation of T-g from much larger systems. In the SG phase, the power-law behavior of the CCF for t much greater thant(w) suggests that the SG phase in short-range Ising models has a rugged phase space.
Scientific journal, English - Non-equilibrium relaxation study for frustrated spin system with successive phase transitions
K Ogawa; Y Ozeki
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 69, 9, 2808-2815, Sep. 2000, The non-equilibrium relaxation method (NER) is applied to a frustrated spin system with competitive interactions. The critical point and critical exponents are estimated accurately for the Blume-Emery-Griffiths model in three dimensions. It is applied to the region where successive transitions of PM-FM-PM-SQ phases occur: we denote paramagnetic (PM), ferromagnetic (Fh I) and staggered quadrupole (SQ) phases. With the analysis for relaxation of fluctuations, we can estimate various critical exponents. The result indicates that all transitions belong to the Ising universality class in three dimensions. It is found that the NER method is useful to analyze the critical phenomena for complex systems in which equilibrium simulation is even difficult.
Scientific journal, English - Nonequilibrium relaxation of fluctuations of physical quantities
N Ito; K Hukushima; K Ogawa; Y Ozeki
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 69, 7, 1931-1934, Jul. 2000, The nonequilibrium relaxation (NER) process of fluctuations of physical quantities is studied simulationally. It is shown that the NER method, which is a convenient technique for studying the phase and transition, is useful not only for identifying the phase and locating the transition point, but also for estimating both static and dynamical exponents. As an example, the cubic-lattice ferromagnetic Ising model is analyzed. The transition inverse-temperature is estimated to be K-c = 0.2216595(15). The exponents of correlation length, magnetization, and specific heat are estimated to be nu = 0.635(5), beta = 0.325(5) and alpha = 0.14(2), respectively. The dynamical exponent z is estimated to be 2.055(10).
Scientific journal, English - Non-Equilibrium Relaxation Method
ISSP Supercomputer Center Activity Report 1999, 37-51, 2000
English - Non-equilibrium relaxation of fluctuation
N Ito; K Ogawa; K Hukushima; Y Ozeki
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE, 138, 138, 555-560, 2000, It is shown that the non-equilibrium relaxation (NER) process of the order-parameter and energy is useful to study the phase transition. By observing the log-derivatives of those decay functions, the critical point is located finely and the critical exponents are estimated accurately The major advantage of NER method is it's simplicity; not only the behavior in the large-size limit can be observed easily, but also it is not necessary to pursue the equilibrium of the system to get information of the final equilibrium state. Applications are expanding from basic systems like Ising ferromagnets, to spin-glass, quantal system, chiral and KT transitions, and so on. Now the NER process of fluctuations is also expected to share those advantages, it is found that the combinations of the NER functions of some fluctuations provide the way to determine static and dynamics critical exponents directly.
Scientific journal, English - Nonequilibrium relaxation method and its applications
N Ito; Y Ozeki
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, WORLD SCIENTIFIC PUBL CO PTE LTD, 10, 8, 1495-1502, Dec. 1999, Nonequilibrium relaxation (NER) process turns out to be an useful method to study phase transition and critical phenomena. The NER method and its applications are reviewed. Characteristic behavior of the local exponent is analyzed with a simple model.
Scientific journal, English - Non-universal critical behavior in the ferromagnetic transition of the +/- J Ising model
N Ito; Y Ozeki; H Kitatani
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 68, 3, 803-810, Mar. 1999, Ferromagnetic (FM) transition of the +/-J Ising model is studied for square and simple-cubic lattices by Monte Carlo simulations. Non-equilibrium relaxation (NER) process of magnetization from the all-aligned spin state is analyzed. The transition temperature is estimated at several values of FM bond concentrations to provide the boundary of the FM phase. The estimated NER exponent of magnetization shows non-universal behavior and it becomes larger smoothly when the transition temperature becomes higher.
Scientific journal, English - 熱平衡を非平衡から調べる－非平衡緩和法
Ito Nobuyasu; Ozeki Yukiyasu; Nonomura Yoshihiko
日本物理学会誌, The Physical Society of Japan (JPS), 54, 5, 336-347, 1999, 非平衡状態から熱平衡状態への緩和の様子から系の熱力学的性質を解析する方法が提唱され, さまざまな問題へと応用が広がっている. 簡便かつ効率的で信頼性も高い「非平衡緩和法」と呼ばれるこの方法の特徴と実例とを計算物理の視点から紹介する.
Japanese - Multicritical dynamics for the +/- J Ising model
Y Ozeki; N Ito
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 31, 24, 5451-5465, Jun. 1998, Exact dynamical properties are discussed for the +/-J Ising model around the multicritical point (MCP). It is found that the relation of relaxations between the non-equilibrium remanent magnetization m(t) and the equilibrium autocorrelation function q(t) at the MCP is different from that at the pure critical point. The dynamic critical exponent for the ferromagnetic ordering defined by m(t) similar to t(-lambda m) and that for the spin glass ordering defined by q(t) similar to t(-lambda q) become identical at the MCP. Accurate numerical calculations for them are performed in two and three dimensions using the non-equilibrium relaxation analysis. The MCP is located at p(mc) = 0.8872 +/- 0.0008 and the exponent is estimated as lambda(m) = lambda(q) = 0.021 +/- 0.001 for the square lattice. They are estimated as p(mc) = 0.7673 +/- 0.0003 and lambda(m) = lambda(q) = 0.090 +/- 0.003 for the simple cubic lattice.
Scientific journal, English - The aging relation for Ising spin glasses
Y Ozeki
JOURNAL OF PHYSICS-CONDENSED MATTER, IOP PUBLISHING LTD, 9, 50, 11171-11177, Dec. 1997, We present a rigorous dynamical relation for aging phenomena-the aging relation-for Ising spin glasses using the method of gauge transformation. The waiting-time dependence of the autocorrelation function in the zero-field-cooling process is equivalent to that in the held-quenching process. There is no aging on the Nishimori line; this provides arguments for dynamical properties of the Griffiths phase and the mixed phase. The present method can be applied to other complex systems with gauge symmetry such as the XY gauge glass.
Scientific journal, English - Symmetry in the phase diagram of the site-random Ising spin glass model in two dimensions
Y Ozeki; Y Nonomura; K Hukushima
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 66, 4, 1165-1174, Apr. 1997, The site-random Ising spin glass model in two dimensions is investigated. The phase diagram is determined in the concentration-temperature plane by the numerical transfer-matrix method. Using the rigorous symmetry found previously, we obtain several exact relations for the order parameters, which provide an insight to the symmetry in the phase diagram.
Scientific journal, English - Phase diagram of three-dimensional site-random Ising model
K Hukushima; Y Nonomura; Y Ozeki; H Takayama
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 66, 1, 215-223, Jan. 1997, The three-dimensional site-random Ising model consisting of two types of magnetic ions, A and B, is investigated by means of the exchange Monte Carlo method. The nearest-neighbor interactions are antiferromagnetic (AF) for the B-B pair and ferromagnetic (FM) otherwise. A uniform FM or AF ordering is found to exist in a wide range of concentration c of A ions, in contrast with the bond-random Ising model such as the +/- J model. The phase diagram is found to be symmetric on the c-T plane, though the ratio of the FM bonds to AF ones is asymmetric with respect to c = 1/2. Spin configurations of degenerate ground states and their cluster structure are also studied. Even in the system with c = 0.55, there exists only a unique rigid cluster which includes about 90% of spins and that cluster shows nonvanishing uniform magnetization. These results strongly suggest that the present model has neither a spin glass phase nor an FM-AF mixed phase, though their existence in a quite narrow region around c = 1/2 has not been completely excluded yet.
Scientific journal, English - Non-frustrated random spin systems with gauge symmetry
Y Ozeki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 29, 18, 5805-5816, Sep. 1996, We introduce a class of random spin systems without frustration, which satisfies the conditions for gauge symmetry. The method of gauge transformation provides several properties on the phase diagram of gauge symmetric models; this method is almost rigorous, while the derivation for the absence of re-entrance contains unproved assumption. In the present random models, the absence of re-entrance can be shown exactly. Furthermore, the phase diagram and the critical properties are exactly related with those in the original pure system. The present random systems correspond to the Mattis model with asymmetric bond distribution in the ising case, and a kind of the gauge glass model in the XY case. In the case of the clock model in two dimensions, we find a new thermodynamic phase which has long-range spin-glass correlation with critical (power-decaying) ferromagnetic correlation.
Scientific journal, English - LONG-RANGE ORDER OF THE SITE-RANDOM SPIN-GLASS MODEL
Y OZEKI; Y NONOMURA
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 64, 9, 3128-3131, Sep. 1995, The site-random Ising spin glass model is investigated. We find a rigorous symmetry for the SG correlation and the free energy, which provides some restrictions in the phase diagram. Using the defect energies calculated by the numerical transfer matrix method, we obtain evidence for the existence of the SG phase in the two-dimensional Ising system. We suggest that the transitions from the FM and the AF phases in the ground state in this model can be explained by the percolated-cluster picture, which is quite different from the frustration picture in the conventional +/-J model.
English - GROUND-STATE PHASE-DIAGRAMS OF THE 2-DIMENSIONAL QUANTUM HEISENBERG SPIN-GLASS MODELS
Y NONOMURA; Y OZEKI
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 64, 8, 2710-2713, Aug. 1995, Ground-state properties of the two-dimensional S=1/2 random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the +/- J model) is the same as that of the corresponding Ising spin glass model, in spite of quantum fluctuation. In the site-random model, the spin glass phase exists at least in the ferro-rich case. In comparison with the corresponding Ising model, the Neel phase of this model becomes much narrower in the ferro-rich case, while it is comparable in the antiferro-rich case.
English - GAUGE TRANSFORMATION FOR DYNAMICAL-SYSTEMS OF ISING SPIN-GLASSES
Y OZEKI
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 28, 13, 3645-3655, Jul. 1995, Dynamical systems of gauge-symmetric Ising spin glasses are investigated by the method of gauge transformation. Several exact relations are derived among dynamical quantities such as the equilibrium autocorrelation function and the non-equilibrium remanent magnetization. The same result as in the static case is obtained in terms of the equivalence of the ferromagnetic and the spin-glass order if the temperature and the randomness satisfy a special condition (Nishimori line). An exact equivalence of non-equilibrium relaxations in the spin-glass phase is derived between the remanent magnetization evolved from the strong-field limit and the autocorrelation function from a supercooled state. We also have a plausible argument for the absence of a re-entrant transition using the present dynamical relations.
Scientific journal, English - Replica Boundary Condition Applied to the ±J Ising Model in Two Dimensions
242, 1995
English - REPLICA BOUNDARY-CONDITION APPLIED TO RANDOM SPIN SYSTEMS
Y OZEKI
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOC JAPAN, 62, 8, 2641-2649, Aug. 1993, We introduce a new boundary condition conjugate to any ordered phases including the spin glass. Using this boundary condition, we calculate an interfacial free energy in random spin systems, which is always non-negative irrespective of the bond configuration. It is possible to calculate a quantity relevant to the spin glass phase as a statistical average of random bond configurations. We apply this method to the asymmetric +/-J Ising model in 2D and 3D. The results are consistent with the previous ones. We observe the scale invariance of the interfacial free energy by the present method at the critical point in 2D (T=0), which is consistent with the power-law decaying spin glass correlation function.
Scientific journal, English - PHASE-DIAGRAM OF GAUGE GLASSES
Y OZEKI; H NISHIMORI
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, IOP PUBLISHING LTD, 26, 14, 3399-3429, Jul. 1993, We introduce a general class of random spin systems which are symmetric under local gauge transformations. Our model is a generalization of the usual Ising spin glass and includes the Z(q), XY, and SU (2) gauge glasses. For this general class of systems, the internal energy and an upper bound on the specific heat are calculated explicitly in any dimensions on a special line in the phase diagram. Although the line intersects a phase boundary at a multicritical point, the internal energy and the bound on the specific heat are found to be written in terms of a simple function. We also show that the boundary between the ferromagnetic and non-ferromagnetic phases is parallel to the temperature axis in the low-temperature region of the phase diagram. This means the absence of re-entrant transitions. All these properties are derived by simple applications of gauge transformations of spin and randomness degrees of freedom.
Scientific journal, English - PHASE-DIAGRAM AND CRITICAL PROPERTIES OF THE ASYMMETRIC MATTIS MODEL
Y OZEKI
JOURNAL OF STATISTICAL PHYSICS, PLENUM PUBL CORP, 71, 3-4, 759-773, May 1993, We extend the well-known Mattis model to the case of asymmetric bond distributions. Although the partition function is identical with that of the pure ferromagnetic Ising model (FIM) when the external field is absent, the response to the external field is nontrivial even at zero field. There are some exact relations between the present model and the FIM in the correlation functions, from which the phase diagram and critical exponents can be determined. Multicritical behavior and some other interesting phenomena typical for a random system are demonstrated by this model.
Scientific journal, English - LOWER CRITICAL DIMENSION OF THE XY SPIN-GLASS
Y OZEKI; H NISHIMORI
PHYSICAL REVIEW B, AMERICAN PHYSICAL SOC, 46, 5, 2879-2884, Aug. 1992, We develop an argument for the absence of spin-glass ordering in short-range vector spin systems with random symmetric exchange interactions in spatial dimension d less-than-or-equal-to 4. The present argument supplements our previous theory; we consider the possibility of divergence in some correlation functions in the limit of small external field. It is also shown that the comment of Schwartz and Young on our previous theory is inappropriate.
Scientific journal, English - INTERFACIAL APPROACH TO D-DIMENSIONAL +/-J ISING-MODELS IN THE NEIGHBORHOOD OF THE FERROMAGNETIC PHASE-BOUNDARY
Y UENO; Y OZEKI
JOURNAL OF STATISTICAL PHYSICS, PLENUM PUBL CORP, 64, 1-2, 227-249, Jul. 1991, Two- and three-dimensional +/- J Ising models in the neighborhood of the ferromagnetic phase (FP) boundary in the concentration-temperature (p-T) plane are studied, investigating the size dependence of interfacial free energies calculated by a transfer matrix method. The p and T dependences of two stiffness exponents relevant to the FP and the nonferromagnetic ordered phase lead to the following results in two dimensions, giving a unified view. It is confirmed that the random antiphase state (RAS) exists in contact with the vertical FP boundary. Spatial fluctuations are dominant near the vertical boundary, which is separated by the Nishimori line from the remaining FP boundary governed by thermal fluctuations. The RAS is a kind of Mattis spin glass such that it changes to the FP smoothly with nonsingular physical connectivity, but with a percolation singularity of its ferromagnetic part. Universal finite-size critical amplitudes are consistent with them. Results in three dimensions give only suggestions which are similar to the two-dimensional results. These results suggest important insight into spin-glass properties in higher dimensions.
Scientific journal, English - GROUND-STATE PROPERTIES OF THE (+/-)J ISING-MODEL IN 2 DIMENSIONS
Y OZEKI
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOCIETY JAPAN KIKAI-SHINKO BUILDING, 59, 10, 3531-3541, Oct. 1990
Scientific journal, English - LONG-RANGE ORDER IN ANTIFERROMAGNETIC QUANTUM SPIN SYSTEMS
Y OZEKI; H NISHIMORI; Y TOMITA
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, PHYSICAL SOCIETY JAPAN, 58, 1, 82-90, Jan. 1989
Scientific journal, English - Addendum to Phase Diagram and Critical Exponents of the $\pm J$ Ising Model in Finite Dimensions by Monte Calro Renormalization Group [56 (1987) 1568]
Ozeki Yukiyasu; Nishimori Hidetoshi
J Phys Soc Jpn, INSTITUTE OF PURE AND APPLIED PHYSICS, 56, 8, 2992-2992, 15 Aug. 1987
English
MISC
- 27pAK-8 Improved Dynamical Scaling Analysis Applied to Confirmation of KT Transition. II
Echinaka Yuki; Ozeki Yukiyasu
The Physical Society of Japan (JPS), 05 Mar. 2014, Meeting abstracts of the Physical Society of Japan, 69, 1, 303-303, Japanese, 1342-8349, 110009834644, AA11439205 - Improved Dynamical Scaling Analysis Applied to Confirmation of KT Transition
Ozeki Yukiyasu; Echinaka Yuki; Matsuda Atsuyuki; Matsuda Daiki
The Physical Society of Japan (JPS), 26 Aug. 2013, Meeting abstracts of the Physical Society of Japan, 68, 2, 260-260, Japanese, 1342-8349, 110009755104, AA11439205 - Improved Dynamical KT Scaling by the use of Bayesian inference and kernel method
Echinaka Yuki; Ozeki Yukiyasu
The Physical Society of Japan (JPS), 26 Aug. 2013, Meeting abstracts of the Physical Society of Japan, 68, 2, 260-260, Japanese, 1342-8349, 110009755103, AA11439205 - 29pXZC-4 Nonequilibrium Relaxation Analysis for Six-States Clock Model in Two Dimensions by the use of the Transition Probability with Modified Rejection Rate II
Ozeki Yukiyasu; Miyao Kanako; Echinaka Yuki; Okumura Kenta
The Physical Society of Japan (JPS), 26 Mar. 2013, Meeting abstracts of the Physical Society of Japan, 68, 1, 412-412, Japanese, 1342-8349, 110009643916, AA11439205 - 20aAC-3 Nonequilibrium Relaxation Analysis for Six-States Clock Model in Two Dimensions by the use of the Transition Probability with Modified Rejection Rate
Ozeki Yukiyasu; Okumura Kenta
The Physical Society of Japan (JPS), 24 Aug. 2012, Meeting abstracts of the Physical Society of Japan, 67, 2, 279-279, Japanese, 1342-8349, 110009602319, AA11439205 - No-equilibrium analysis with mixed phase initialization : Application to first order phase transitions
KASONO Katsumi; OSEKI Yukiyasu
The Physical Society of Japan (JPS), 13 Aug. 2002, Meeting abstracts of the Physical Society of Japan, 57, 2, 208-208, Japanese, 1342-8349, 110009720511, AA11439205 - 24pWL-9 No-equilibrium analysis of first order phase transitions using mixed start method.
KASONO Katsumi; OZEKI Yukiyasu
The Physical Society of Japan (JPS), 01 Mar. 2002, Meeting abstracts of the Physical Society of Japan, 57, 1, 235-235, Japanese, 1342-8349, 110009771156, AA11439205 - 24aXY-3 Non-equilibrium Relaxation Analysis for Two Dimensional Frustrated XY Models
Ozeki Yukiyasu; Ito Nobuyasu
The Physical Society of Japan (JPS), 01 Mar. 2002, Meeting abstracts of the Physical Society of Japan, 57, 1, 230-230, Japanese, 1342-8349, 110009771141, AA11439205 - 25aWL-9 NER Study on Icing Spin Glass
Ito Nobuyasu; Ozeki Yukiyasu
The Physical Society of Japan (JPS), 01 Mar. 2002, Meeting abstracts of the Physical Society of Japan, 57, 1, 247-247, Japanese, 1342-8349, 110009771201, AA11439205 - 30p-TB-5 Long Range Order in Antiferromagnetic Quantum Spin Systems in Two Dimensions
Ozeki T.; Nishimori H.
The Physical Society of Japan (JPS), 28 Mar. 1989, 年会講演予稿集, 44, 3, 398-398, Japanese, 110009793685, AN10453938
Books and other publications
- Recent Development in Nonequilibrium Relaxation Method
English, Computer Simulation Studies in Condensed Matter Physics XIV (Springer-Verlag), 2002 - Non-equilibrium Relaxation Study of The Phase Transition
English, Proceeding of the 8th Asia-Pacific Physics Conference (World Scentific), 2001 - Simulation Study on Phase Transition using Dynamical Behavior
English, Computer Simulation Studies in Condensed-Matter Physics XIII (Springer-Verlag), 2001 - Non-Equilibrium Relaxation of Fluctuations and Its Application to Critical Phenomena
English, Journal of Physical Society of Japan Supplement, 2000 - The Method of Gauge Transformation in Random Spin Systems
English, Statistical Models, Yang-Baxter Equation and Related Topics(World Scientific), 1996 - Phase Diagram of the Site-Random Ising Spin Glass Model
English, Coherent Approaches to Fluctuations (World Scientific), 1996 - On The Two-Dimensional Site-Random Quantum Heisenberg Spin Glass Model
English, Coherent Approaches to Fluctuations (World Scientific), 1996
Lectures, oral presentations, etc.
- スピン・カイラルグラス転移の解明に向けた、非平衡過程における相関長を用いた動的臨界指数の解析
寺澤雄介; 尾関之康
Oral presentation, Japanese, 日本物理学会２０２４年春季大会, Peer-reviewed
21 Mar. 2024
18 Mar. 2024- 21 Mar. 2024 - 機械学習を用いた非平衡緩和法の臨界指数評価法における系統的外挿法の確立
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会２０２４年春季大会
18 Mar. 2024
18 Mar. 2024- 21 Mar. 2024 - ガウス過程回帰による非平衡緩和解析の改良
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会2023年春季大会
25 Mar. 2023
22 Mar. 2023- 25 Mar. 2023 - ガウス過程回帰によるゆらぎの緩和解析の臨界指数評価
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０２２年秋季大会, 日本物理学会, 東京工業大学 大岡山キャンパス, Domestic conference
13 Sep. 2022 - 改良された動的スケーリング解析による3 次元イジングスピングラスの相図と臨界現象
寺澤雄介; 尾関之康
Oral presentation, Japanese, 日本物理学会,第７７回年次大会, 日本物理学会, 遠隔開催, Domestic conference
17 Mar. 2022 - KT転移系へのevent-chain 法の適用におけるサイズ効果
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０２１年秋季大会, 日本物理学会, 遠隔開催, Domestic conference
21 Sep. 2021 - Explosive Percolation の臨界指数のさらなる評価
萩原健太; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０２１年秋季大会, 日本物理学会, 遠隔開催, Domestic conference
20 Sep. 2021 - event-chain 法を適用した連続スピン系における ゆらぎの緩和の振る舞い
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会,第７６回年次大会, 日本物理学会, 遠隔開催, Domestic conference
12 Mar. 2021 - Explosive Percolation の臨界指数評価
萩原健太; 尾関之康
Oral presentation, Japanese, 日本物理学会,第７６回年次大会, 日本物理学会, 遠隔開催, Domestic conference
12 Mar. 2021 - 非平衡緩和法によるExplosive Percolationモデルのスケーリング解析
萩原健太; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０２０年秋季大会, 日本物理学会, 遠隔開催, Domestic conference
11 Sep. 2020 - Event-chain法による動的臨界指数の比較
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０２０年秋季大会, 日本物理学会, 遠隔開催, Domestic conference
10 Sep. 2020 - 磁場中反強磁性三角格子Heisenberg模型における対称性の破れの非平衡緩和解析 II
尾関之康; 村山一明
Oral presentation, Japanese, 日本物理学会,第７５回年次大会, 日本物理学会, 名古屋大学（現地開催中止）, Domestic conference
19 Mar. 2020 - Event-chain法による非平衡緩和解析の有効性
長田優馬; 尾関之康
Oral presentation, Japanese, 日本物理学会,第７５回年次大会, 日本物理学会, 名古屋大学（現地開催中止）, Domestic conference
18 Mar. 2020 - 磁場中反強磁性三角格子Heisenberg模型における対称性の破れの非平衡緩和解析
村山一明; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０１９年秋季大会, 日本物理学会, 岐阜大学柳戸キャンパス, Domestic conference
10 Sep. 2019 - 動的スケーリング法による２次元フラストレートハイゼンベルグ模型の臨界普遍性の数値解析II
飛世崚吾; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０１８年秋季大会, 日本物理学会, 同志社大学京田辺キャンパス, Domestic conference
11 Sep. 2018 - 動的スケーリング法による２次元フラストレートハイゼンベルグ模型の臨界普遍性の数値解析
飛世崚吾; 尾関之康
Oral presentation, Japanese, 日本物理学会,第７３回年次大会, 日本物理学会, 東京理科大学野田キャンパス, Domestic conference
24 Mar. 2018 - 改良された動的スケーリング法による三角格子反強磁性ハイゼンベルグ模型のトポロジカル相転移解析
飛世崚吾; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０１７年秋季大会, 日本物理学会, 岩手大学, Domestic conference
24 Sep. 2017 - 改良された動的スケーリング法による２次元フラストレー卜ＸＹ模型の非平衡緩和解析
矢島優里; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０１６年秋季大会, 日本物理学会, 金沢大学
16 Sep. 2016 - ２次元古典XZ模型の臨界現象の非平衡緩和解析
尾関之康
Oral presentation, Japanese, 日本物理学会,第７１回年次大会, 日本物理学会, 関西大学, Domestic conference
Mar. 2016 - カーネル法を利用した非平衡緩和解析のさらなる改良
尾関之康; 恵知中悠貴
Oral presentation, Japanese, 日本物理学会,２０１５年秋季大会, 日本物理学会, 関西大学
Sep. 2015 - 二次元RP2模型の非平衡緩和解析
松田篤幸; 恵知中悠貴; 尾関之康; 富田裕介
Oral presentation, Japanese, 日本物理学会,第６９回年次大会, 日本物理学会, 東海大学, Domestic conference
Mar. 2014 - 改良された動的スケーリング解析によるKT転移の判別II
恵知中悠貴; 尾関之康
Oral presentation, Japanese, 日本物理学会,第６９回年次大会, 日本物理学会, 東海大学
Mar. 2014 - ベイズ推定とカーネル法を用いた動的スケーリング法の改良
恵知中悠貴; 尾関之康
Oral presentation, Japanese, 日本物理学会,２０１３年秋季大会
Sep. 2013 - 改良された動的スケーリング解析によるKT転移の判別
尾関之康; 恵知中悠貴; 松田篤幸; 松田大輝
Oral presentation, Japanese, 日本物理学会,２０１３年秋季大会
Sep. 2013 - 棄却率を調整した遷移確率による２次元６状態クロック模型の非平衡緩和解析II
尾関之康; 宮尾加奈子; 恵知中悠貴; 奥村健太
Oral presentation, Japanese, 日本物理学会,第６８回年次大会
Mar. 2013 - 棄却率を調整した遷移確率による２次元６状態クロック模型の非平衡緩和解析
尾関之康; 奥村健太
Oral presentation, Japanese, 日本物理学会,２０１２年秋季大会
Sep. 2012 - ２次元ランダムXY模型のKT相における臨界指数の非平衡緩和解析
酒井拓也; 尾関之康
Oral presentation, Japanese, 日本物理学会,第65回年次大会
Mar. 2010 - 3次元ゲージグラス模型におけるスピングラス転移の非平衡緩和解析
萩原敦; 尾関之康
Oral presentation, Japanese, 日本物理学会,2009年秋季大会
Sep. 2009 - Isingスピングラス模型におけるスピングラス相と臨界普遍性の非平衡緩和解析
菅谷太一; 萩原敦; 尾関之康
Oral presentation, Japanese, 日本物理学会,第64回年次大会
Mar. 2009 - ２次元ゲージグラス模型のKT相内における臨界指数の非平衡緩和解析
尾関之康; 酒井拓也
Oral presentation, Japanese, 日本物理学会,第64回年次大会
Mar. 2009 - Phase diagrams and critical properties for the $\pm J$ Ising model in two and three dimensions
Yukiyasu Ozeki
Invited oral presentation, English, Multicritical Behaviour of Spin Glasses and Quantum Error Correcting Codes (MBQEC), Tokyo Inst. of Tech., Tokyo, International conference
Nov. 2008 - ランダム系の臨界普遍性の非平衡緩和解析II
尾関之康; 四柳智司; 菅谷太一
Oral presentation, Japanese, 日本物理学会,第６３回年次大会
Mar. 2008 - ランダム系の臨界普遍性の非平衡緩和解析
尾関之康
Public symposium, Japanese, 計算物性物理学の進展, 東京大学物性研究所, 千葉県柏市
Nov. 2007 - ３次元ゲージグラス模型の臨界普遍性I
尾関之康; 四柳智司; 菅谷太一
Oral presentation, Japanese, 日本物理学会,第６２回年次大会
Sep. 2007 - 3次元離散ゲージグラス模型のフラストレーション効果
四柳智司; 尾関之康
Oral presentation, Japanese, 日本物理学会,2007年春季大会
Mar. 2007 - 非平衡緩和法による離散ゲージグラス模型の解析
尾関之康
Public symposium, Japanese, 物性研短期研究会 「計算物性科学におけるスーパーコンピュータ利用の現状と展望」, 東京大学物性研究所, 千葉県柏市
Dec. 2006 - 2次元Clock Gauge Glass模型の相図とKT相の安定性II
尾関之康; 四柳智司
Oral presentation, Japanese, 日本物理学会,2006年秋季大会
Sep. 2006 - Nonequilibrium relaxation studies for frustrated spin systems with Kosterlitz-Thouless transition
Yukiyasu Ozeki
Invited oral presentation, English, U.S.-Japan Bilateral Seminar, Hawaii, USA, International conference
Jul. 2006 - ２次元Clock Gauge Glass模型の相図とKT相の安定性
尾関之康
Oral presentation, Japanese, 日本物理学会,第６１回年次大会
Mar. 2006 - ２次元ゲージグラス系のKosterlitz-Thouless相転移
尾関之康
Oral presentation, Japanese, 日本物理学会,2005年秋季大会
Sep. 2005 - 量子スピングラスにおけるゲージ理論
森田悟史; 尾関之康; 西森秀稔
Oral presentation, Japanese, 日本物理学会,2005年秋季大会
Sep. 2005 - Gauge theory for gauge glass systems
Y. Ozeki
Invited oral presentation, English, Statistical Physics of Disordered Systems and its Applications, Roma, International conference
Sep. 2005 - Nonequilibrium Relaxation Study on Universality Classes
Y. Ozeki
Invited oral presentation, English, The 1st International Workshop Hangzhou 2004 on Simulational Physics, Zhejiang University, 抗州、中国, International conference
Nov. 2004 - ２次元ランダムZq模型の非平衡緩和解析
尾関之康
Oral presentation, Japanese, 日本物理学会,2004年秋季大会
Sep. 2004
Research Themes
- 改良された動的スケーリングが導くトポロジカル相転移の高精度解析法と普遍性の研究
尾関之康
Principal investigator
01 Apr. 2019 - 31 Mar. 2023 - カーネル法による動的スケーリング解析の改良と非平衡緩和法の新展開
01 Apr. 2015 - 31 Mar. 2019 - Theoretical Study of Spin Glasses Using Methods of Information Science
NISHIMORI Hidetoshi
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Tokyo Institute of Technology, Grant-in-Aid for Scientific Research (C), I have investigated the problem of spin glasses with emphasis on relations with information science. The potentially approximate analysis of replica method for the CDMA performance has been checked by rigorous approaches and I have shown that the result is valid in spite of use of the replica method. The problem of subset sum has been investigated and a serious problem has been pointed out in a previous study of this issue. The deficiency has been improved and a new insight into the system behavior has been established. Multispin-interacting system has been studied in the mean-field level to establish that the ratio of spin-glass-like term and ferromagnetic term plays a crucial role in the structure of the phase diagram., 12640369
2000 - 2002 - エイジング関係式から見たスピングラスのダイナミクスの研究
尾関 之康
日本学術振興会, 科学研究費助成事業, 東京工業大学, 奨励研究(A), エイジング関係式と非平衡緩和法を利用して、スピングラス転移と動的クロスオーバー領域の解析を行った。 エイジング関係式によって、動的相関関数のシミュレーションが容易になり、非平衡緩和法と呼ばれる新しい方法を組み合わせて、スピングラス転移の解析を行った。この方法は、秩序化した状態からの秩序変数の非平衡緩和を数値的にシミュレートする方法で、統計平均はMCステップを重ねて行うのではなく独立にサンプリングする。このため、系の平衡化から解放されるのでメモリーが許す最大の格子サイズで計算できる、MCステップは動的性質が判る程度の小ステップで十分、各サンプルは独立なの臨界点でもサンプルは少なくて済む、等の利点がある。従来、30^3程度の格子が限界であったが、今回は最大で160^3の格子の解析が可能になり、これまで曖昧だったサイズ効果の不安を取り除く事ができた。 常磁性相、強磁性相、スピングラス相が会合する多重臨界点での動的性質を導出し、動的臨界現象の大域的な変遷を理解することに成功した。残留磁化m(t)は強磁性相では秩序変数に収束し、平衡自己相関関数q(t)はスピングラス相で秩序変数に収束する。両者の緩和指数λ_mとλ_qは、強磁性臨界点ではλ_q=2λ_mの関係にあるが、多重臨界点でλ_q=λ_mと変化することが明らかになった。また、多重臨界点では、強磁性秩序とスピングラス秩序の弱臨界指数(動的指数を含む)が一致する事も示された。これらは動的臨界現象の普遍性の変化であり、今後の研究の端緒となることが期待される。, 09740309
1997 - 1998 - 短距離スピングラス模型における数値計算の大型化と新しい境界条件の導入
尾関 之康
日本学術振興会, 科学研究費助成事業, 東京工業大学, 重点領域研究, スピングラスの理論的描像は、EdwardsとAnderson模型を基礎とした平均場理論によって、統一的に理解されるようになった。そして、現実的な短距離模型において、この平均場描像がどのように実現され、また、修正されるかが、その後の研究者の興味の中心である。 界面自由エネルギーの方法は、規則系の相転移を解析する手段として開発され、非常の有効である事が確認されている。この方法は、常磁性相、強磁性相、スピングラス相が共存するランダム系の相転移の解析にも有効である事が示されていた。しかし、スピングラス秩序に共役な境界条件を用いていなかったので、スピングラス相の解析には、界面自由エネルギーの分布の幅が必要になり、分布の平均値で解析される強磁性相転移との精度の差に問題が残った。 本研究では、ランダムな秩序に共役な境界条件を提案し、スピングラス相など任意の秩序相の解析に有効な界面自由エルギーを求めた。この方法で得られる界面自由エネルギーは、常に 【numerical formula】 が成立するので、その平均値でランダムな秩序を調べる事が可能になり、従来の方法に比べて精度の良い解析が期待される。この方法を±JIsing模型に適用した結果、以前の結果と矛盾しない結果が得られ、方法の有効性が示された。また、二次元の基底状態において、以前から指摘されていた臨界的な振舞いを示唆する結果が初めて得られた。今後、この境界条件を応用したランダム系の解析が盛んに行われることが期待される。, 04231212
1992 - 1992 - 相転移と秩序相に対する界面的方法の開発と応用
上野 陽太郎; 尾関 之康; 岡本 清美; 小野 いく郎
日本学術振興会, 科学研究費助成事業, 東京工業大学, 重点領域研究, ひねりの方法(一般性があるので界面の方法を改称)をモンテカルロシミューレーションや厳密な数値計算によって以下の問題に適用し、所期の成果を挙げた。()内は分担者及び協力者。 1)ひねりの方法自体の性質の検討(塩田、上野、加園):2次元Isingモデル等で調べた結果、剛性指数は有限サイズスケーリングを示し、転移点は上限を与え、普遍振幅は理論値とよく一到すると判明。また、我々の計算方法はMon & Jasnowのより非常に優れていると判断された。 2)3次元一般化6状態クロック(GCL)モデルにおける不完全秩序相(10P)の相転移(上野、加園):前年度に続き10Pを研究した結果、柔らかい剛性(剛性指数が約1.2)を示す10Pと通常の固い秩序相の間の相転移には、驚くべきことに対称性の変化がないことが初めて見いだされた。スピン配列等からもこの転移がトポロジカルと推測された. 3)GCLモデルの幾何学的記述wall percolationの数値解析(上野、里村):理論的定式化により、10Pは隣接した状態にあるクラスター間のwallがpercolationしていることによって特徴づけられることが判明。クラスター解析の結果、10Pがwall percolation状態であると確認される。 4)1次相転移に対するひねりの方法の適用(小野、加園、上野):ひねりの方法を使って1次転移に適用した結果、エネルギー増分の有限サイズスケーリングを開発し、それが非常に有効であることが判明。 5)1次元量子スピン系の相転移(岡本、野村、西野、上野):ひねりの方法が初めて量子系のs=1/2競合Heisenbergモデルに適用されたが、fluid相とdimer相間の相転移点が良し精度で決まることが判明。理論で予測された有限サイズスケーリングのlog補正項の存在も明らかになる。更に、励起伏態の性質を利用によって、この転移点から非常に高い精度によって決定された。, 04231211
1992 - 1992 - 相転移に対するモンテカルロ界面的方法の開発と応用
上野 陽太郎; 岡本 清美; 田口 善弘; 尾関 之康; 小野 〓郎
日本学術振興会, 科学研究費助成事業, 東京工業大学, 重点領域研究, 界面の方法をモンテカルロシミュレ-ションや厳密な数値計算によって以下の問題に適用し、開発と応用を行った。()内は分担者及び協力してくれた院生である。 1)3次元高縮退系における不完全秩序相(加園、上野)。一般化6状態クロックモデルを研究した結果、パラメ-タのある領域では2種類の不完全秩序相(IOP)の存在が、そしてそれが消える領域では1次転移の出現が判明した。IOPの興味ある性質も明らかになった。 2)1次元量子スピン系の相転移(岡本、上野)。この方法が初めて量子系のs=1/2競合Heisenbergモデルに適用されたが、fluid相とdimer相間の相転移点が極めて精度よく決まることが判明した。また、理論で予測された有限サイズスケ-リングのlog補正項の存在も明らかになった。 3)ランダムスピン系(尾関、上野)。2次元±JIsingモデルにスタガ-ド磁場を加えると、フェロ領域が2つの異なる性質を持つことが得られた。これは先に得たMattisスピングラスであることと関係あることを示唆している。 4)弱い1次転移と2次転移を区別する問題(山県、加園)。2次元Pottsモデルに対して転移点近傍に現れる界面吸着の幅を計算すると、1次転移で期待されるサイズ依存性が得られた。従って、吸着の幅は一般にこの問題の解決に有力であることを示唆している。 5)KosterlitzーThouless転移とmassless相の性質(山県、小野)。2次元6状態クロックモデルに対し、massless相では界面自由エネルギ-がスケ-ル不変になることが得られ、またKT転移点でのuniversal Jumpが示唆された。 6)界面の方法の基礎付け(上野)。系全体の界面自由エネルギ-が、相転移と秩序相の研究において基本的物理量となることを、経路積分として考えることによって理論的に明らかされた。更に従来利用されてきたそれの様々な重様な性質の正当性も証明された。, 03247212
1991 - 1991