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ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE

FARRUKH MUKHAMEDOV

Department of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, 700095, Tashkent, Uzbekistan

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and

UTKIR ROZIKOV

Institute of Mathematics, 29, F. Hodjaev str., Tashkent, 700143, Uzbekistan

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https://doi.org/10.1142/S0219025705001974Cited by:48 (Source: Crossref)

Abstract

We consider a nearest-neighbor inhomogeneous p-adic Potts (with q≥2 spin values) model on the Cayley tree of order k≥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∉pℕ then there is unique Gibbs measure for any k≥1 and ∀ J_xy with | J_xy |< p^{-1/(p -1)}. (ii) For q∈p ℕ, p≥3 one can choose J_xy and k≥1 such that there exist at least two Gibbs measures which are translation-invariant.

Keywords:

AMSC: 46S10, 82B26, 12J12

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