麦克斯韦-玻尔兹曼分布在易辛模型中的应用

Application of Maxwell-Boltzmann distribution in Ising model

麦克斯韦-玻尔兹曼分布给出了系统在任一微观状态下的玻尔兹曼概率,从而可以计算系统中宏观观测量的统计平均值.但在实际计算中,由于系统可能微观状态数随系统晶格格点数增大而指数增大,往往无法进行计算.本文以易辛模型为例,介绍了如何从玻尔兹曼概率的角度研究系统可能微观状态的演化过程,从而可以只考虑高概率的微观状态.使用该方法,研究了二维易辛模型的平均每自旋的基态能量和平均每自旋的磁化率随温度的变化关系.

Maxwell-Boltzmann distribution has broad application prospect in statistical physics.This distribution gives the Boltzmann probability of any microstate of the system,so we can calculate the statistical average of the macroscopic observation of the system.However,most of the real calculations are hard to be done,due to the fact that the number of all the possible microstates increases exponentially with the number of the lattice sites.In this paper,we take the Ising model as an example,to introduce the evolution of the possible microstates from the view of the Boltzmann probability,hence we only need to consider the microstates with large Boltzmann probability.In this way,we study the ground-state energy per site and magnetization per site as functions of temperature,in a two-dimensional Ising model.