A p-Adic Generalized Gibbs Measure for the Ising Model on a Cayley Tree

Abstract

We consider a p-adic Ising model on the Cayley tree of order k ≥ 2. We completely describe all p-adic-translation-invariant generalized Gibbs measures for k = 3. Moreover, we show the existence of a phase transition for the p-adic Ising model for any k ≥ 3 if p ≡ 1 (mod 4).