arXiv:cond-mat/9705236 · Journal of Physics A Mathematical and General

Monte Carlo simulation of the short-time behaviour of the dynamicXY-model

Keisuke Okano, Lothar Schülke, K. Yamagishi, Bo Zheng

Published Jul 7, 1997• 23 citations

Abstract

Dynamic relaxation of the XY-model quenched from a high temperature state to the critical temperature or below is investigated with Monte Carlo methods. When a non-zero initial magnetization is given, in the short-time regime of the dynamic evolution the critical initial increase of the magnetization is observed. The dynamic exponent is directly determined. The results show that the exponent varies with respect to the temperature. Furthermore, it is demonstrated that this initial increase of the magnetization is universal, i.e. independent of the microscopic details of the initial configurations and the algorithms.

DOI: 10.1088/0305-4470/30/13/009

Related papers

Critical Relaxation and Critical Exponents 1

H. J. Luo, Bo Zheng

Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The dynamic critical exponent z and the static exponent η are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to those measured with traditional methods.

Jan 1, 199810 citations

Monte Carlo simulation of universal short-time behaviour in critical relaxation

Zhibing Li, Uwe Ritschel, Bo Zheng

The time evolution of the three-dimensional critical Ising model relaxing from a non-equilibrium initial state is studied by means of Monte Carlo simulation. We observe the characteristic initial increase of the (spatially) averaged magnetization predicted by Janssen et al. The exponent theta ' that governs the initial behaviour is determined, and the dependence of the long-time linear decay on the initial magnetization, m 0 , is analysed. Our simulation corroborates earlier results derived from continuum models.

arXiv:cond-mat/9409058Journal of Physics A Mathematical and GeneralNov 7, 199483 citations

Critical Relaxation and Critical Exponents

H. J. Luo, B. Zheng

Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behavior is observed. The dynamic critical exponent z and the static exponent η are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to those measured with traditional methods.

arXiv:cond-mat/9812147Modern Physics Letters BJun 20, 199720 citations

Generalized Dynamic Scaling for Critical Relaxations

Bo Zheng

The dynamic relaxation process for the two dimensional Potts model at criticality starting from an initial state with very high temperature and arbitrary magnetization is investigated with Monte Carlo methods. The results show that there exists universal scaling behavior even in the short-time regime of the dynamic evolution. In order to describe the dependence of the scaling behavior on the initial magnetization, a critical characteristic function is introduced.

arXiv:cond-mat/9607013Physical Review LettersJul 22, 199647 citations

Short-time critical dynamics of the three-dimensional Ising model

A Jaster, J. Mainville, L Schülke +1 more

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent of the critical initial increase and the dynamic exponent z , the static critical exponents and as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.

arXiv:cond-mat/9808131Journal of Physics A Mathematical and GeneralJan 1, 199976 citations

Non-equilibrium critical dynamics of the two-dimensional XY model with Hamiltonian equations of motion

A Asad, Bo Zheng

Non-equilibrium critical dynamics of the two-dimensional XY model is investigated with Hamiltonian equations of motion. Critical relaxation starting from both ordered and random states is carefully analyzed, and the short- time dynamic scaling behavior is revealed. Logarithmic corrections to scaling are detected for relaxation with a random initial state, while power-law corrections to scaling are observed for relaxation with an ordered initial state. The static exponent η and dynamic exponent z are determined around and below the Kosterlitz-Thouless phase transition temperature. Our results show that the deterministic dynamics described by Hamiltonian equations is in the same universality class as the stochastic dynamics described by Monte Carlo algorithms and Langevin equations.

Journal of Physics A Mathematical and TheoreticalAug 1, 20079 citations