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Sibirsk. Mat. Zh., 2016, Volume 57, Number 4, Pages 928–939 (Mi smj2793)  

$p$-adic hard-core model with three states on a Cayley tree

O. N. Khakimov

Institute of Mathematics, Tashkent, Uzbekistan

Abstract: We examine the $p$-adic hard-core model with three states on a Cayley tree. Translationinvariant and periodic $p$-adic Gibbs measures are studied for the hard-core model for $k=2$. We prove that every $p$-adic Gibbs measure is bounded for $p\ne2$. We show in particular that there is no strong phased transition for a hard-core model on a Cayley tree of order $k$.

Keywords: Cayley tree, configuration, Gibbs measure, hard-core model, translation-invariant measure, $p$-adic number.

DOI: https://doi.org/10.17377/smzh.2016.57.414

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English version:
Siberian Mathematical Journal, 2016, 57:4, 726–734

Bibliographic databases:

UDC: 517.98+530.1
Received: 14.09.2015

Citation: O. N. Khakimov, “A $p$-adic hard-core model with three states on a Cayley tree”, Sibirsk. Mat. Zh., 57:4 (2016), 928–939; Siberian Math. J., 57:4 (2016), 726–734

Citation in format AMSBIB
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\by O.~N.~Khakimov
\paper A~$p$-adic hard-core model with three states on a~Cayley tree
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 4
\pages 928--939
\mathnet{http://mi.mathnet.ru/smj2793}
\crossref{https://doi.org/10.17377/smzh.2016.57.414}
\elib{http://elibrary.ru/item.asp?id=27380085}
\transl
\jour Siberian Math. J.
\yr 2016
\vol 57
\issue 4
\pages 726--734
\crossref{https://doi.org/10.1134/S0037446616040145}
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