Geodesic
The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 165-172

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We consider fertile Hard-Core (HC) models with activity parameter $\lambda>0$ and four states on the Cayley tree of order two. It is known that there are three types of such models. In this paper for each of these models the uniqueness of the translation-invariant Gibbs measure is proved.
Keywords: Cayley tree, HC-model, Gibbs measure, translation-invariant measures.
Mots-clés : configuration 
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     author = {Rustam M. Khakimov},
     title = {The uniqueness of the translation-invariant {Gibbs} measure for four state {HC-models} on a {Cayley} tree},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Rustam M. Khakimov. The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 165-172. http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a5/