Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

Nonequilibrium relaxation analysis of gauge glass models in two dimensions

Yukiyasu Ozeki, Keita Ogawa

Published Jun 14, 2005• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.71.220407

Related papers

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

Yukiyasu Ozeki, Satoshi Yotsuyanagi, Takuya Sakai +1 more

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 η 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 η 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.

Physical Review E•Feb 18, 2014•6 citations

Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition

Yukiyasu Ozeki, Keita Ogawa, Nobuyasu Ito

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) approximately t(-lambda(T)). Only outside the KT phase, an asymptotic single exponential decay is observed. Using a standard scaling form m(t)=tau(-lambda)(-)m(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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 14, 2003•41 citations

Dynamical scaling analysis of phase transition and critical properties for the RP2 model in two dimensions

Yukiyasu Ozeki, Atsuyuki Matsuda, Yuki Echinaka

The phase transition and critical properties for the RP^{2} model in two dimensions is investigated by means of the nonequilibrium relaxation method (NER) together with the dynamical scaling analysis. The relaxation of nematic order from the all-aligned state is observed by Monte Carlo simulations. The comparison of types of the asymptotic form of the relaxation time around the transition point is considered by the dynamical scaling analysis, which clearly discriminates the Kosterlitz-Thouless (KT)-type transition from the second-order one. Using the relaxation of fluctuation, the static critical exponent η and the dynamical one z, which are only the intrinsic exponents for the KT transition, are estimated at and below the KT transition temperature. The result shows similar behaviors with those observed in the KT phase for the ferromagnetic XY model in two dimensions, which has been recognized as a typical KT system, and reveals the confirmation of the present KT transition.

Physical review. E•Jan 11, 2019•6 citations

Dynamical scaling analysis on critical universality class for fully frustrated XY models in two dimensions

Yukiyasu Ozeki, Yuri Yajima, Yuka Nakamura

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-Ising-type 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.

Physical review. B./Physical review. B•Mar 31, 2020•6 citations

Effects of discreteness on gauge glass models in two and three dimensions

Satoshi Yotsuyanagi, Yusuke Suemitsu, Yukiyasu Ozeki

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/q2. 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.

Physical Review E•Apr 23, 2009•2 citations

Nonequilibrium relaxation method

Yukiyasu Ozeki, Nobuyasu Ito

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.

Journal of Physics A Mathematical and Theoretical•Jul 19, 2007•84 citations
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=1000L=1000L=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.
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 η 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 η 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.
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) approximately t(-lambda(T)). Only outside the KT phase, an asymptotic single exponential decay is observed. Using a standard scaling form m(t)=tau(-lambda)(-)m(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.
The phase transition and critical properties for the RP^{2} model in two dimensions is investigated by means of the nonequilibrium relaxation method (NER) together with the dynamical scaling analysis. The relaxation of nematic order from the all-aligned state is observed by Monte Carlo simulations. The comparison of types of the asymptotic form of the relaxation time around the transition point is considered by the dynamical scaling analysis, which clearly discriminates the Kosterlitz-Thouless (KT)-type transition from the second-order one. Using the relaxation of fluctuation, the static critical exponent η and the dynamical one z, which are only the intrinsic exponents for the KT transition, are estimated at and below the KT transition temperature. The result shows similar behaviors with those observed in the KT phase for the ferromagnetic XY model in two dimensions, which has been recognized as a typical KT system, and reveals the confirmation of the present KT transition.
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-Ising-type 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.
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/q2. 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.
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.