玻茨模型

在统计力学中，玻茨模型（Potts模型）是易辛模型的推广，它描述晶格上的自旋。玻茨模型可应用于铁磁性和固态物理学。

定义

玻茨模型的哈密頓量是：

$H_{p}=-J_{p}\sum _{(i,j)}\delta (s_{i},s_{j})$

其中 $s_{i}=1,\ldots ,q$ 是晶格上的自旋变数， δ(s_i, s_j) 是克罗内克函数。当 s_i = s_j 时，该函数等于1，否则等于0。

q=2的玻茨模型等于易辛模型（J_p = -2J_c ）。

有时会引入磁场h：

$F=\beta H_{g}=-\beta \sum _{(i,j)}J_{ij}\delta (s_{i},s_{j})-\sum _{i}h_{i}s_{i}$

其中 β=1/kT 的T是温度，k是波茲曼常數。

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