In this paper we prove that for any integer \(q\ge 5\), 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.

中文翻译：

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无穷$$\Delta $$上反铁磁Potts模型吉布斯测度的唯一性-大$$\Delta $$的正则树

在本文中，我们证明对于任何整数\(q\ge 5\) ，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都有唯一的吉布斯测度\ (w\in [1-q/\Delta ,1)\)，前提是\(\Delta \)足够大。这证实了一个长期以来的民间传说猜想。