Geodesic
$p$-Adic Gibbs measures for the~hard core model with three states on the~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 68-82

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We study $p$-adic hard core models with three states on the Cayley tree. It is known that there are four types of such models. We find conditions that must be imposed on the order $k$ of the Cayley tree and on the prime $p$ for a translation-invariant $p$-adic Gibbs measure to exist.
Keywords: Cayley tree, Gibbs measure, hard core $G$-model, translation-invariant measure, $p$-adic number.
Mots-clés : configuration 
@article{TMF_2013_177_1_a1,
     author = {O. N. Khakimov},
     title = {$p${-Adic} {Gibbs} measures for the~hard core model with three states on {the~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {68--82},
     publisher = {mathdoc},
     volume = {177},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a1/}
}
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O. N. Khakimov. $p$-Adic Gibbs measures for the~hard core model with three states on the~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 177 (2013) no. 1, pp. 68-82. http://geodesic.mathdoc.fr/item/TMF_2013_177_1_a1/