On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree

Details On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree

2005-10-06

arxiv.org/abs/math-ph/0510024v2

Published in Infin. Dim.Anal.Quant. Probab.Rel.Top.8(2005), No. 2, 277-290

Physics

Mathematical Physics

15 pages

Scientific paper

We consider a nearest-neighbor inhomogeneous $p$-adic Potts (with $q\geq 2$ spin values) model on the Cayley tree of order $k\geq 1$. The inhomogeneity means that the interaction $J_{xy}$ couplings depend on nearest-neighbors points $x, y $ of the Cayley tree. We study ($p-$ adic) Gibbs measures of the model. We show that (i) if $q\notin p\mathbb{N}$ then there is unique Gibbs measure for any $k\geq 1$ and $\forall J_{xy}$ with $|J_{xy}|

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