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arXiv:cond-mat/9812147 · Modern Physics Letters B

Critical Relaxation and Critical Exponents

H. J. Luo, B. Zheng

Published Jun 20, 1997• 20 citations
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Abstract

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.

DOI
10.1142/s0217984997000761

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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.
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We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a method to measure both the dynamic and static critical exponents are reported, based on the finite-size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted independently, while the static exponents \ensuremath{\beta}/\ensuremath{\nu} and \ensuremath{\nu} are obtained from the time evolution of the magnetization and its higher moments. \textcopyright{} 1996 The American Physical Society.
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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.