3维有限宽度Ising模型的模拟计算  

Simulation of 3-dimensional finite Ising model

作　　者：曹斌[1,2] 杨薇[1,2] 崔春翔[1,2] 

机构地区：[1]河北省新型功能材料重点实验室,天津300130 [2]河北工业大学材料学院,天津300130

出　　处：《中国科学：物理学、力学、天文学》2017年第6期26-36,共11页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:51271070);河北省自然科学基金(编号:E2014202008;E2016202406);国际科技合作计划项目(编号:2010DFA51920);河北省高等学校科学技术研究重点项目(编号:ZH2011202);河北省新型功能材料重点实验室资助

摘　　要：本文发展了一种计算方法将3维Ising模型的转化矩阵V_1替换为一个秩更小的转化矩阵.将转化矩阵V_1表示为基矢量的线性叠加,我们发现可以将基矢量分为几组,一个基矢量与V_1的矩阵乘积可以被表示为同组基矢量的线性叠加.以此为原理,我们建立了一个新的转化矩阵V_2来描述一个基矢量和V_1的乘积与同组基矢量之间的关系,而一组包含基矢量的个数就是V_2的秩.V_2的秩比V_1小得多并包含最大特征值.本文用此方法计算了单位比热和单位磁矩.结果显示存在一对温度和磁场的组合使比热取得最大值,当N_1N_2增加时,比热峰值也增加.We have developed a method to change the transfer matrix V1 of 3D Ising model into a much smaller transfer matrix. I11 can be written as the linear combination of basic vectors. We discover that these basic vectors can be divided into several groups. The point product of one basic vector and V2 can be written as the linear combination of basic vectors from the same group. Based on that, we establish a new transfer matrix V2 to describe the relationship between basic vectors of the same group. The number of members from the same group is the order of V2. V2 is much smaller than V1 and contains the largest eigenvalue of V1. We use this method to calculate the specific heat and magnetic momentum per atom. The results show that there＇s a pair of temperature and magnetic field strength that can make the specific heat get to its maximum value. When N1N2 increases, the maximum value of specific heat increases too.

关 键 词：ISING模型 磁序 比热 统计力学 

分 类 号：O411[理学—理论物理]