In this paper we prove that for any integer $q\geq 5$, the anti-ferromagnetic $q$-state Potts model on the infinite $\Delta$-regular tree has a unique Gibbs measure for all edge interaction parameters $w\in [1-q/\Delta,1)$, provided $\Delta$ is large enough. This confirms a longstanding folklore conjecture.

翻译：在本文中,我们证明,对于任何整数$q\geq 5美元,在无限的$Delta$-正则树上的反地磁元美元-状态波茨模型,对所有边缘互动参数都有一个独特的Gibbs测量值[1-q/\Delta,1]$,只要$\Delta$足够大。这证实了长期的民俗猜想。