Geodesic
Gibbs measures for fertile hard-core models on the Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 340-352 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study fertile hard-core models with the activity parameter $\lambda>0$ and four states on the Cayley tree. It is known that there are three types of such models. For each of these models, we prove the uniqueness of the translation-invariant Gibbs measure for any value of the parameter $\lambda$ on the Cayley tree of order three. Moreover, for one of the models, we obtain critical values of $\lambda$ at which the translation-invariant Gibbs measure is nonunique on the Cayley tree of order five. In this case, we verify a sufficient condition (the Kesten–Stigum condition) for a measure not to be extreme.
Keywords: Cayley tree, fertile graph, hard-core model, Gibbs measure, translation-invariant measure.
Mots-clés : configuration 
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}
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R. M. Khakimov. Gibbs measures for fertile hard-core models on the Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 340-352. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a11/

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