ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE

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.

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DOI

10.1142/s0219025705001974

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