三维Ising模型矩阵解法的简化与近似解

3D ISING MODEL, SIMPLIFICATION OF MATRIX METHOD AND AN APPROXIMATE SOLUTION

利用Ising模型在无外场周期边界条件下的哈密顿量的对称性,对矩阵进行块对角化,严格求得2×2×n简单立方晶格Ising模型的解析解,对其他两种自旋集团较小的情况的热力学函数自由能进行数值计算,在数据拟合的基础上提出一种近似解.

With the symetries of Hamitonian in Ising model of cubic lattice under periodic boundary conditions and without external field, the matrices of the proplems are block diagonalised. The problem of 2×2×n cubic lattice is rigorously solved. Free energy of two other simple cases are computed, an approximate solution is proposed based on numerical results.