Translation-invariant and weakly periodic Gibbs measures for HC-models on a Cayley tree

Abstract: In this paper is studied HC-models on a Cayley tree. two states HC-model on a Cayley tree and Under some conditions on parameters of the two state HC-model we prove existence exactly two of the weakly periodic (non periodic) Gibbs measures. Furthermore, it considered translation-invariant Gibbs measures for fertile four state HC-models and for one of them it proved the non-uniqueness of the translation-invariant Gibbs measure.