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Preprints Archive: Abstract of IC2010035 (2010)

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On P-adic quasi Gibbs measures for Q+1-state Potts model on the Cayley tree

by Farrukh Mukhamedov

Document info: Pages 15, Figures 0.

In the present paper we introduce a new class 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 $p$-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, U.A. Rozikov, Indag. Math. N.S. 15 (2005) 85-100], since $q$ 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).

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