Monte Carlo Simulation of the Short-time Behaviour of the Dynamic XY Model

TL;DR

This paper uses Monte Carlo simulations to study the early-time behavior of the dynamic XY model, revealing a universal initial magnetization increase and temperature-dependent dynamic exponents.

Contribution

It provides the first direct determination of the dynamic exponent θ in the short-time regime of the XY model and demonstrates its universality and temperature dependence.

Findings

Critical initial increase of magnetization observed.

Dynamic exponent θ varies with temperature.

Universality of initial magnetization increase confirmed.

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 $\theta$ is directly determined. The results show that the exponent $\theta$ 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.