# 易辛模型

## 定義

$E=-\sum_{ij} J_{ij}s_i s_j-H\sum_i s_i$

$J_{ij}$是耦合矩陣。

$J_{ij} > 0$ 表示自旋交互作用為鐵磁性
$J_{ij} < 0$ 表示自旋交互作用為反鐵磁性
$J_{ij} = 0$ 表示自旋間無交互作用。

## 一維易辛模型

$E = -J \sum _{i=1}^N s_i s_{i+1}+H \sum _{i=1}^N s_i$

$M (H,T)=\frac{\sinh (\beta H )}{\sqrt{\sinh ^2(\beta H )+e^{-4\beta J }}}$.

$M (0,T)=0$.

## 延伸閱讀

1. Kerson Huang, Introduction to Statistical Physics.
2. I. A. Stepanov. Exact Solutions of the One-Dimensional, Two-Dimensional, and Three-Dimensional Ising Models. – Nano Science and Nano Technology: An Indian Journal. 2012. Vol. 6. No 3. 118 - 122. The paper is on the Journal’s website with a free access.