Geodesic
The~uniqueness condition for a~weakly periodic Gibbs measure for the~hard-core model
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 1, pp. 60-70

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We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant.
Keywords: Cayley tree, hard-core model, Gibbs measure, periodic measure, weakly periodic measure.
Mots-clés : configuration 
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     author = {U. A. Rozikov and R. M. Khakimov},
     title = {The~uniqueness condition for a~weakly periodic {Gibbs} measure for the~hard-core model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {60--70},
     publisher = {mathdoc},
     volume = {173},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_1_a2/}
}
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U. A. Rozikov; R. M. Khakimov. The~uniqueness condition for a~weakly periodic Gibbs measure for the~hard-core model. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 1, pp. 60-70. http://geodesic.mathdoc.fr/item/TMF_2012_173_1_a2/