标题： 平移不变和周期性吉布斯测度在Cayley树上的Potts模型 显示英文标题

标题： Translation-invariant and periodic Gibbs measures for Potts model on a Cayley tree

摘要： 在本文中研究了三状态铁磁Potts模型在三阶Cayley树上的情况，并给出了平移不变的Gibbs测度的显式公式。此外，我们证明了在反铁磁Potts模型的参数满足某些条件时，零外部场下的q状态Cayley树的order$k>2$上，恰好存在2(2^q-1)个周期性（非平移不变）的Gibbs测度。 显示英文摘要

摘要： In this paper is studied ferromagnetic three states Potts model on a Cayley tree of order three and we give explicit formulas for translation-invariant Gibbs measures. Furthermore, we show that under some conditions on the parameter of the antiferromagnetic Potts model with q-states with zero external field on the Cayley tree of order $k>2$, there are exactly 2(2^q-1) periodic (non translation-invariant) Gibbs measures.