Uniqueness of the Gibbs measure for the anti-ferromagnetic Potts model on the infinite $\Delta$-regular tree for large $\Delta$

Abstract

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.

21 pages, 1 figure. Small corrections based on referee comments. Published in Journal of Statistical Physics

References in corpus (2)

• Gibbs measures of Potts model on Cayley trees: a survey and applications
• Uniqueness of the Gibbs measure for the $4$-state anti-ferromagnetic Potts model on the regular tree