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Phase transitions for -adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the -state
-adic Potts model over the Cayley tree of order three. We consider a more
general notion of -adic Gibbs measure which depends on parameter
\rho\in\bq_p. Such a measure is called {\it generalized -adic quasi Gibbs
measure}. When equals to -adic exponent, then it coincides with the
-adic Gibbs measure. When , then it coincides with -adic quasi
Gibbs measure. Therefore, we investigate two regimes with respect to the value
of . Namely, in the first regime, one takes for some
J\in\bq_p, in the second one . In each regime, we first find
conditions for the existence of generalized -adic quasi Gibbs measures.
Furthermore, in the first regime, we establish the existence of the phase
transition under some conditions. In the second regime, when we prove the existence of a quasi phase transition. It turns out that
if and \sqrt{-3}\in\bq_p, then one finds the existence
of the strong phase transition.Comment: 27 page