The Calculations of 3-Dimensional Ising Model of Finite Width  

作　　者：Bin Cao Wei Yang Chunxiang Cui 

机构地区：[1]Key Lab.for New Type of Functional Materials in Hebei Province,Tianjin 300130,China [2]School of Material Science and Engineering,Hebei University of Technology,Tianjin 300130,China

出　　处：《Journal of Harbin Institute of Technology(New Series)》2016年第4期59-66,共8页哈尔滨工业大学学报（英文版）

基　　金：Sponsored by the National Natural Science Foundation of China(Grant No.51271070);the Natural Science Foundation of Hebei Province(Grant No.E2014202008,E2016202406);the National Science and Technology Program-International Collaborative Research Project(Grant No.2010DFA51920);the Key Program from the science and Technology Research for Colleges and Universities in Hebei Province(Grant No.ZH2011202);the Key Lab.for New Type of Functional Materials in Hebei Province

摘　　要：In order to calculate 3-dimensional Ising model,we develop a method to build a much smaller transfer matrix containing the largest eigenvalue from the original 2^(N_1N_2) × 2^(N_1N_2) matrix V_1. Firstly,the transfer matrix V_1 is written as the linear combination of several basic vectors. Secondly,we divide the basic vectors into several subgroups. The multiplication of a basic vector and V_1 can be written as the linear combination of basic vectors from the same subgroup. Finally,we use a new transfer matrix V_2 to describe the relationship between basic vectors of the same subgroup.V_2 is much smaller than the original transfer matrix and contains the largest eigenvalue of V_1.We use this method to calculate the specific heat per atom Cpaand the magnetic momentum per atom Mpa. The results show that there exists a pair of temperature and magnetic field intensity where the specific heat gets to its maximum value. When N_1N_2 increases,the maximum value of specific heat becomes larger.In order to calculate 3-dimensional Ising model,we develop a method to build a much smaller transfer matrix containing the largest eigenvalue from the original 2^(N_1N_2) × 2^(N_1N_2) matrix V_1. Firstly,the transfer matrix V_1 is written as the linear combination of several basic vectors. Secondly,we divide the basic vectors into several subgroups. The multiplication of a basic vector and V_1 can be written as the linear combination of basic vectors from the same subgroup. Finally,we use a new transfer matrix V_2 to describe the relationship between basic vectors of the same subgroup.V_2 is much smaller than the original transfer matrix and contains the largest eigenvalue of V_1.We use this method to calculate the specific heat per atom Cpaand the magnetic momentum per atom Mpa. The results show that there exists a pair of temperature and magnetic field intensity where the specific heat gets to its maximum value. When N_1N_2 increases,the maximum value of specific heat becomes larger.

关 键 词：ISING model magnetic ORDERING Specific heat STATISTICAL MECHANICS 

分 类 号：T0[一般工业技术]