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：本文证明：对于任意整数$q\geq 5$，只要$\Delta$足够大，无限$\Delta$-正则树上的反铁磁$q$-态Potts模型对所有边相互作用参数$w\in [1-q/\Delta,1)$均具有唯一的Gibbs测度。这一结果证实了长期存在的学界猜想。