Periodic quasi Gibbs measures for the $p$-adic Potts model with an external field

Abstract

In the present paper, we study $G_2$-periodic $p$-adic quasi Gibbs measures for the $p$-adic Potts model with an external field on a Cayley tree of order two. We find $G_2$-periodic (non-translation-invariant) $p$-adic quasi Gibbs measures. Moreover, for the corresponding model, we show that if $|q(q-1)|_p=1$, $\sqrt{1-q}\in \mathbb Q_p$ then a phase transition occurs; If $|q|_p<1$, a quasi phase transition occurs.