On p-Adic Quasi Gibbs Measures for q

In the present paper we introduce a new kind of p-adic measures, associated with q + 1-state Potts model, called p-adic quasi Gibbs measure, which is totally different from the p-adic Gibbs measure. We establish the existence of p-adic quasi Gibbs measures for the model on a Cayley tree. If q is divisible by p, then we prove the occurrence of a strong phase transition. If q and p are relatively prime, then there is a quasi phase transition. These results are totally different from the results of [F. M. Mukhamedov and U. A. Rozikov, Indag. Math. N. S. 15, 85-100 (2005)], since when q is divisible by p, which means that q + 1 is not divided by p, so according to a main result of the mentioned paper, there is a unique and bounded p-adic Gibbs measure (different from p-adic quasi Gibbs measure)