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

Acta Physica Sinica

A numerical study on the aging of two-dimensional spin systems

Lei Xiao-wei, Bo Zheng, Ying He-Ping, (1)浙江大学浙江近代物理中心,杭州 310027; (2)重庆文理学院物理与信息工程系,重庆 402160;浙江大学浙江近代物理中心,杭州 310027

Published Jan 1, 2007• 2 citations
Publisher

Abstract

With a large-scale Monte Carlo simulation, the aging of the two-dimensional dynamic Ising and XY models is numerically studied. Starting from a disordered state, the systems are quenched to critical temperature Tc and then evolve according to dynamics of model A. By calculating the autocorrelation function A(t,t′) we observe the aging phenomenon for both spin systems. Then, relatively accurate values of the dynamic critical exponent λc and z are estimated. Especially, we confirm that for the two-dimensional XY model, there is a strong logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered.

DOI
10.7498/aps.56.1713

Related papers

Study for aging phenomena of two-dimensional Ising and XY model

Lei Xiao-wei

With dynamic Monte Carlo simulations,aging phenomena of two-dimensional Ising model and dynamic XY model were studied numerically.Systems were quenched to their critical point from a disordered initial state.The autocorrelation function was calculated by heat-bath algorithm.Critical exponents were also calculated.It was confirmed that for the 2D XY model,there is a logarithmic correction to scaling.The universality proposal and their scale relation in aging phenomena were predicted.The scale relation agreed with renormalization group calculations.

Journal of Zhejiang University(Science Edition)•Jan 1, 2007•0 citations

Aging Phenomenon of 2D XY Model Starting from an Ordered Intial State

Xiaoyu Zhao

With Monte Carlo simulation method,the aging phenomenon of the 2D XY model is numerically studied.Starting from an ordered initial state,the system is suddenly quenched to critical temperature Tc.The two-time autocorrelation function A(t,t') is measured.For a dynamic process with an ordered initial state,the difficult problem is that accurate analysis is lagging behind the Monte Carlo simulation study.So many activities have been devoted to dynamic scaling form.According to the numerical experimental data of 2D XY non-equilibrium system,the relation between A(t,t') and ratio of spatial correlation length is detected.The aging phenomenon exhibits a dynamic scaling behavior induced by the time correlation.The aging phenomenon is characterized by the dynamic scale invariance.The aging phenomenon of 2D XY model is confirmed.Especially,the correction of scaling behavior is numerically verified,the form of dynamic scaling of A(t,t') is more creditable than existing literatures.For a dynamic process starting from an ordered initial state,the scaling form assumption fits the numerical data well.The scaling form holds not only at lower temperatures but also around Tc.This is because of the simulation temperature is close to the critical temperature.Based on the dynamic scaling,the experimental data indicate that more accurate values of the critical exponents can be obtained.In addition,the data collapse phenomenon is observed.

Keji daobao•Jan 1, 2011•0 citations

Short-time critical dynamics and aging phenomena in the two-dimensional XY model

X. W. Lei, Bo Zheng

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.

Physical Review E•Apr 12, 2007•33 citations

Logarithmic corrections in the aging of the fully-frustrated Potts model

Christophe Chatelain

We study the aging of the two-dimensional fully-frustrated Ising and threestate Potts models by means of Monte Carlo simulations. The system is initially prepared at infinite temperature and then quenched either at its critical temperature or in the low-temperature phase for the three-state Potts model. Autocorrelation and response functions are shown to satisfy the scaling behavior conjectured for aging ferromagnets if one assumes the existence of logarithmic corrections. The dynamical and autocorrelation exponents are compatible with � = d and z = 2 for the Ising model and probably the threestate Potts model both at and below Tc. The fluctuation-dissipation ratio goes asymptotically to different non-trivial values at Tc and does not vanish below Tc.

•Jul 13, 2007•0 citations

Logarithmic corrections in the ageing of the fully frustrated Ising model

Jean‐Charles Walter, Christophe Chatelain

We study the dynamics of the critical two-dimensional fully frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value z c = 2. In a second step, the system is prepared in the paramagnetic phase and then quenched at its critical temperature T c = 0. Numerical evidence for the existence of logarithmic corrections in the ageing regime is presented. These corrections may be related to the topological defects observed in other fully frustrated models. The autocorrelation exponent is estimated to be λ = d as for the Ising chain quenched at T c = 0.

arXiv:0707.1959•Journal of Statistical Mechanics Theory and Experiment•Jul 4, 2008•6 citations

Spin Systems far from Equilibrium: Aging and Dynamic Phase Transition

Hyunhang Park

Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.

•Mar 22, 2013•0 citations
With a large-scale Monte Carlo simulation, the aging of the two-dimensional dynamic Ising and XY models is numerically studied. Starting from a disordered state, the systems are quenched to critical temperature Tc and then evolve according to dynamics of model A. By calculating the autocorrelation function A(t,t′) we observe the aging phenomenon for both spin systems. Then, relatively accurate values of the dynamic critical exponent λc and z are estimated. Especially, we confirm that for the two-dimensional XY model, there is a strong logarithmic correction to scaling in the dynamic relaxation starting from a completely disordered.
With dynamic Monte Carlo simulations,aging phenomena of two-dimensional Ising model and dynamic XY model were studied numerically.Systems were quenched to their critical point from a disordered initial state.The autocorrelation function was calculated by heat-bath algorithm.Critical exponents were also calculated.It was confirmed that for the 2D XY model,there is a logarithmic correction to scaling.The universality proposal and their scale relation in aging phenomena were predicted.The scale relation agreed with renormalization group calculations.
With Monte Carlo simulation method,the aging phenomenon of the 2D XY model is numerically studied.Starting from an ordered initial state,the system is suddenly quenched to critical temperature Tc.The two-time autocorrelation function A(t,t') is measured.For a dynamic process with an ordered initial state,the difficult problem is that accurate analysis is lagging behind the Monte Carlo simulation study.So many activities have been devoted to dynamic scaling form.According to the numerical experimental data of 2D XY non-equilibrium system,the relation between A(t,t') and ratio of spatial correlation length is detected.The aging phenomenon exhibits a dynamic scaling behavior induced by the time correlation.The aging phenomenon is characterized by the dynamic scale invariance.The aging phenomenon of 2D XY model is confirmed.Especially,the correction of scaling behavior is numerically verified,the form of dynamic scaling of A(t,t') is more creditable than existing literatures.For a dynamic process starting from an ordered initial state,the scaling form assumption fits the numerical data well.The scaling form holds not only at lower temperatures but also around Tc.This is because of the simulation temperature is close to the critical temperature.Based on the dynamic scaling,the experimental data indicate that more accurate values of the critical exponents can be obtained.In addition,the data collapse phenomenon is observed.
With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.
We study the aging of the two-dimensional fully-frustrated Ising and threestate Potts models by means of Monte Carlo simulations. The system is initially prepared at infinite temperature and then quenched either at its critical temperature or in the low-temperature phase for the three-state Potts model. Autocorrelation and response functions are shown to satisfy the scaling behavior conjectured for aging ferromagnets if one assumes the existence of logarithmic corrections. The dynamical and autocorrelation exponents are compatible with � = d and z = 2 for the Ising model and probably the threestate Potts model both at and below Tc. The fluctuation-dissipation ratio goes asymptotically to different non-trivial values at Tc and does not vanish below Tc.
We study the dynamics of the critical two-dimensional fully frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value z c = 2. In a second step, the system is prepared in the paramagnetic phase and then quenched at its critical temperature T c = 0. Numerical evidence for the existence of logarithmic corrections in the ageing regime is presented. These corrections may be related to the topological defects observed in other fully frustrated models. The autocorrelation exponent is estimated to be λ = d as for the Ising chain quenched at T c = 0.
Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.