广义Potts模型的相关不等式：广义Griffiths不等式
Correlation Inequalities for Generalized Potts Model: General Griffiths' Inequalities
摘要：
本文将Ising模型中考虑的相关不等式推广到q-Potts模型。考虑了任意自旋相互作用的广义Potts模型。我们用中心集$F=\{-(q-1)/2,-(q-3)/2,... ,(q-3)/2,(q-1)/2\}$替换自旋值集$F=\{1,2,..., q\}$。设$N$是具有$n$顶点的一维晶格的子集，$\g=(\s_1,\s_2,...,\s_n):N \to F^c$是一种构型，其中${(\s_i)}_\g$是出现在$\g$中的第i个自旋（分量）的数，$\s_i$是在$\g$处的值为${(\s_i)}_\g$的随机变量。为任何列表$R$定义$\s^R=\prod_{i \in R}\s_i$，其中任何$i \in R$都意味着$i \in N$。我们首先证明$<\s^R > \ge 0$，然后我们证明，对于任何两个列表$R$和$S$，我们有$<\s^R \s^S >- < \s^R > < \s^S > \ge 0$。
英文摘要：
In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values $F=\{1,2,..., q\}$ by the centered set $F=\{-(q-1)/2,-(q-3)/2,... ,(q-3)/2,(q-1)/2\}$. Let $N$ be the subset of one-dimensional lattice with $n$ vertices, $\g=(\s_1,\s_2,...,\s_n):N \to F^c$ be a configuration where ${(\s_i)}_\g$ is the number which appears as the ith spin (component) in $\g$ and $\s_i$ be a random variable whose value at $\g$ is ${(\s_i)}_\g$. Define $\s^R=\prod_{i \in R}\s_i$ for any list $R$ where any $i \in R$ implies that $i \in N$. We first prove that $<\s^R > \ge 0$ then we prove that for any two lists $R$ and $S$, we have $<\s^R \s^S >- < \s^R > < \s^S > \ge 0$.
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