In this paper we prove that for any integer q ≥ 5, the anti-ferromagnetic q-state Potts model on the infinite -regular tree has a unique Gibbs measure for all edge interaction parameters w ∈ [Δ − q/, Δ), provided is large enough. This confirms a longstanding folklore conjecture.

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Journal of Statistical Physics

Bencs, F., de Boer, D., Buys, P., & Regts, G. (2023). Uniqueness of the Gibbs measure for the anti-ferromagnetic
Potts model on the Infinite Δ-regular tree for large Δ. Journal of Statistical Physics, 190, 140:1–140:24. doi:10.1007/s10955-023-03145-z