Gibbs Measures of the Blume–Emery–Griffiths Model on the Cayley Tree

Abstract

In this paper we consider the Blume–Emery–Griffiths model on Cayley trees. We reduce the problem of describing the splitting Gibbs measures of the Blume–Emery–Griffiths model to the description of the solutions of some algebraic equation. Also, we analyse the set of translation-invariant splitting Gibbs measures for a two parametric BEG model on Cayley trees.