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.

arXiv comment21 pages, 1 figure. Small corrections based on referee comments. Published in Journal of Statistical Physics

References in corpus (9)

• The multivariate Tutte polynomial (alias Potts model) for graphs and matroids
• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models
• Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
• Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree
• On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field
• Gibbs measures of Potts model on Cayley trees: a survey and applications
• Correlation decay and partition function zeros: Algorithms and phase transitions
• Uniqueness of the Gibbs measure for the $4$-state anti-ferromagnetic Potts model on the regular tree