On Phase Transitions for $P$-Adic Potts Model with Competing Interactions on a Cayley Tree

Details On Phase Transitions for $P$-Adic Potts Model with Competing Interactions on a Cayley Tree On Phase Transitions for $P$-Adic Potts Model with Competing Interactions on a Cayley Tree

2005-12-07

arxiv.org/abs/math-ph/0512018v2

Proceedings of the '2nd International Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005) published by

Physics

Mathematical Physics

12 pages, to appear in the Proceedings of the '2nd International Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 S

Scientific paper

10.1063/1.2193118

In the paper we considere three state $p$-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the $p$-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if $p=3$ for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a $p$-adic context. Namely, if $p\neq 3$ then there is only a unique Gibbs measure the model.

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