Four competing interactions for models with uncountable set of spin values on the Cayley Tree

F. H. Haydarov

Published 2015-09-16Version 1

In this paper we consider four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order two. We reduce the problem of describing the "splitting Gibbs measures" of the model to the description of the solutions of some nonlinear integral equation and consider Gibbs measures for Ising and Potts models. Also we show that periodic Gibbs measures for given models are either translation-invariant or periodic with period two.