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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 1, Pages 185–196
DOI: https://doi.org/10.17377/smzh.2018.59.116 (Mi smj2964) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Weakly periodic Gibbs measures for HC-models on Cayley trees

R. M. Khakimov

Namangan State University, Namangan, Uzbekistan
Full-text PDF (358 kB) Citations (8)
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DOI: https://doi.org/10.17377/smzh.2018.59.116
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.
Received: 07.12.2015
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 1, Pages 147–156
DOI: https://doi.org/10.1134/S0037446618010160
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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