Geodesic
Extremality of the~unique translation-invariant Gibbs measure for hard-core models on the~Cayley tree of order $k=3$
Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 1, pp. 112-124

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We study fertile hard-core models with three states and an activity parameter $\lambda>0$ on the Cayley tree of order $k=3$. It is known that there are four types of such models. For two of them, we find the regions where the unique translation-invariant Gibbs measure is (not) extremal. For one of the considered models, we find the conditions under which the extremal measure is not unique.
Keywords: Cayley tree, hard-core model, fertile graph, Gibbs measure, translation-invariant measure, measure extremality.
Mots-clés : configuration 
@article{TMF_2021_206_1_a5,
     author = {R. M. Khakimov and K. O. Umirzakova},
     title = {Extremality of the~unique translation-invariant {Gibbs} measure for hard-core models on {the~Cayley} tree of order $k=3$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {112--124},
     publisher = {mathdoc},
     volume = {206},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a5/}
}
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R. M. Khakimov; K. O. Umirzakova. Extremality of the~unique translation-invariant Gibbs measure for hard-core models on the~Cayley tree of order $k=3$. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 1, pp. 112-124. http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a5/