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arXiv · 2203.15457

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

Ferenc Bencs·David de Boer·Pjotr Buys·Guus Regts
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Abstract

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

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Ferenc Bencs, David de Boer, Pjotr Buys, Guus Regts. 2022-03-29. Uniqueness of the Gibbs measure for the anti-ferromagnetic Potts model on the infinite $\Delta$-regular tree for large $\Delta$. https://doi.org/10.1007/s10955-023-03145-z

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