二维完全阻挫XY模型的动力学指数

The dynamic exponent of two-dimensional fully frustrated XY model

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless(KT)型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上(T>TKT),独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下(T<TKT)测量的结果一致.

With a large-scale Monte Carlo simulation, non-equilibrium dynamics of the two-dimensional fully frustrated XY model is investigated. We tackle the Kosterlitz-Thouless phase transition. Starting from an ordered initial state, we study the dynamic evolution of the magnetization as well as a specifically defined Binder cumulant. From the dynamic scaling ansatz, we extract the correlating time of the dynamics and the spatial correlation length of the equilibrium state. The dynamic exponent z is determined with relatively high accuracy. Especially, we suggest and demonstrate how one may directly measure the dynamic exponent z above TKT from the scaling fit of the Binder cumulant. These results indicate that the dynamic exponent z fluctuates around z = 2, and this is consistent with that observed at temperatures below the transition temperature TKT.