Weakly periodic p-adic quasi-Gibbs measures for the Potts model on a Cayley tree

In the present paper, we study the weakly periodic p-adic quasi-Gibbs measures for the three-state Potts model on a Cayley tree of order two. Under some conditions, we show there exist 14 weakly periodic (non-periodic) p-adic quasi-Gibbs measures. Moreover, if \(p=3\) $p=3$ then there are six weakly periodic p-adic Gibbs measures for this model. We also prove that if \(p\ne 3\) $p\ne 3$ then a phase transition occurs for the Potts model on a Cayley tree of order two.