Uniqueness of the Gibbs measure for the $4$-state anti-ferromagnetic Potts model on the regular tree

David de Boer, Pjotr Buys, Guus Regts

We show that the $4$-state anti-ferromagnetic Potts model with interaction parameter $w\in (0,1)$ on the infinite $(d+1)$-regular tree has a unique Gibbs measure if $w\geq 1-\frac{4…