On Gibbs measures of P-adic Potts model on the cayley tree

Abstract

We consider a nearest-neighbor p-adic Potts (with q ≥ 2 spin values and coupling constant J ϵ Q p ) model on the Cayley tree of order k ≥ 1. It is proved that a phase transition occurs at k = 2, q ϵ p N and p ≥ 3 (resp. q ϵ 2 2 N , p = 2). It is established that for p-adic Potts model at k ≥ 3 a phase transition may occur only at q ϵ p N if p ≥ 3 and q ϵ 2 2 N if p = 2.