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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 Gibbsmeasure for all edge interaction parameters $w\in [1-q/\Delta,1)$, provided$\Delta$ is large enough. This confirms a longstanding folklore conjecture.

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