混合自旋伊辛模型中损伤扩散的蒙特卡罗模拟

The Monte Carlo simulation on the damage spreading in a mixed spin Ising model

利用损伤扩散技术和Metropolis抽样方法,研究了二维正方格子上具有晶格场作用的混合自旋伊辛模型的动力学.模拟结果显示,损伤和磁化强度具有相似的温度依赖关系.在给定晶格场强度下损伤随温度的升高而减小,并且存在一个临界温度.当温度高于该临界温度时,具有不同初始组态的两系统相空间轨迹重合.系统的临界温度随着晶格场强度的减小而增加.当晶格场足够弱时,系统退化为纯粹的伊辛模型;反之,随着晶格场强度的增强系统的相变温度连续减小到0.没有观察到一阶相变,因而不存在三临界点现象.

The dynamics of a mixed spin Ising model with a crystal field on the square lattice are investigated by using the damage spreading technique and Metropolis sampling method. The sim- ulation results reveal that the damage （Hamming distance） shows a very similar temperature de- pendence to that of the magnetization. The Hamming distance decreases with temperature and there is a critical temperature, beyond which the phase space trajectories of two systems with dif- ferent initial configurations consist with each other. The critical temperature increases when the strength of the crystal field decreases, and the mixed spin Ising model will degenerate to a stand- ard Ising model under a considerable weak crystal field. The critical temperature decreases to zero continuously as the strength of the crystal filed increases. There is not any first order phase tran- sition observed in the above process and thus no tricritical point exists in this system.