We consider the bipartite Potts model in which interaction strengths depend only on the groups the particles belong to. We first rigorously compute the exact value of the free energy, then put forward two scaling limit theorems for the joint distribution of two empirical vectors which serve as order parameters. It turns out that the limit distribution can be Gaussian or the exponential distribution of higher order under different conditions.

中文翻译：

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二分 Potts 模型的极限定理

我们考虑二分 Potts 模型，其中相互作用强度仅取决于粒子所属的组。我们首先严格计算自由能的精确值，然后针对作为阶参数的两个经验向量的联合分布提出两个标度极限定理。事实证明，极限分布可以是高斯分布，也可以是不同条件下的高阶指数分布。