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

03/29/2022

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by   Ferenc Bencs, et al.

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In this paper we prove that for any integer q≥ 5, the anti-ferromagnetic q-state Potts model on the infinite Δ-regular tree has a unique Gibbs measure for all edge interaction parameters w∈ [1-q/Δ,1), provided Δ is large enough. This confirms a longstanding folklore conjecture.