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Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 185–196 (Mi smj2964)  

Weakly periodic Gibbs measures for HC-models on Cayley trees

R. M. Khakimov

Namangan State University, Namangan, Uzbekistan

Abstract: We study hard-core (HC) models on Cayley trees. Given a $2$-state HC-model, we prove that exactly two weakly periodic (aperiodic) Gibbs measures exist under certain conditions on the parameters. Moreover, we consider fertile $4$-state HC-models with the activity parameter $\lambda>0$. The three types of these models are known to exist. For one of the models we show that the translationinvariant Gibbs measure is not unique.

Keywords: Cayley tree, configuration, HC-model, fertile graph, Gibbs measure, weakly periodic measure, translation-invariant measure.

DOI: https://doi.org/10.17377/smzh.2018.59.116

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English version:
Siberian Mathematical Journal, 2018, 59:1, 147–156

Bibliographic databases:

UDC: 517.98
Received: 07.12.2015

Citation: R. M. Khakimov, “Weakly periodic Gibbs measures for HC-models on Cayley trees”, Sibirsk. Mat. Zh., 59:1 (2018), 185–196; Siberian Math. J., 59:1 (2018), 147–156

Citation in format AMSBIB
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\by R.~M.~Khakimov
\paper Weakly periodic Gibbs measures for HC-models on Cayley trees
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 1
\pages 185--196
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\crossref{https://doi.org/10.17377/smzh.2018.59.116}
\elib{http://elibrary.ru/item.asp?id=32824602}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 1
\pages 147--156
\crossref{https://doi.org/10.1134/S0037446618010160}
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