Abstract

The expressions for average products of three neighboring spins in the Ising model have been found on lattices with coordination numbers 3 and 4 as functions of temperature and spontaneous magnetization. These expressions are used to compare the exact solution for the Ising model on a square lattice and the solutions found by approximate methods. A method of improving approximate methods is proposed for applying, in particular, to the Bethe approximation and to a change in the critical index of the temperature dependence of the spontaneous magnetization.

中文翻译：

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Ising 模型中自旋相关性的近似计算

摘要

Ising 模型中三个相邻自旋的平均乘积表达式已在配位数为 3 和 4 的晶格上发现，作为温度和自发磁化的函数。这些表达式用于比较 Ising 模型在方格上的精确解和通过近似方法找到的解。提出了一种改进近似方法的方法，尤其适用于贝特近似和自发磁化的温度依赖性的临界指数的变化。