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

Abstract

In this paper we consider a p-adic Ising model on the Cayley tree of order k ≥ 2. We give full description of all p-adic translation-invariant generalized Gibbs measures for k = 3. Moreover, we show the existence of phase transition for p-adic Ising model for any k ≥ 3 when p ≡ 1(mod 4).Mathematics Subject Classification: 37B05, 37B10,12J12, 39A70

Translation‐invariant generalized P‐adic Gibbs measures for the Ising model on Cayley trees

“…Finally, by (31) and (32), we arrive at (30) which completes the proof. Now we are going to find fixed points of f , k on Z * p .…”

“…In what follows, we restrict ourselves to the p-adic Ising model on the Cayley tree, since this model has broad theoretical and practical applications. 25 We note that in previous studies, [26][27][28][29][30][31][32][33][34][35][36][37][38]72 an analysis of the set of special kinds of p-adic Gibbs measures has been started. However, in the present article, we are going to study phase transitions within generalized p-adic Gibbs measures which have not been previously investigated.…”