On Phase Transitions for $P$-Adic Potts Model with Competing Interactions on a Cayley Tree
Mathematical Physics
2009-11-11 v2 math.MP
Number Theory
Abstract
In the paper we considere three state -adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the -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 for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a -adic context. Namely, if then there is only a unique Gibbs measure the model.
Cite
@article{arxiv.math-ph/0512018,
title = {On Phase Transitions for $P$-Adic Potts Model with Competing Interactions on a Cayley Tree},
author = {Farrukh Mukhamedov and Utkir Rozikov and Jose Fernando F. Mendes},
journal= {arXiv preprint arXiv:math-ph/0512018},
year = {2009}
}
Comments
12 pages, to appear in the Proceedings of the '2nd International Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005) published by AIP Conference Proceedings