Rustam M. Khakimov, “The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 165

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Journal of Siberian Federal University. Mathematics & Physics, 2015, Volume 8, Issue 2, Pages 165–172 (Mi jsfu418)

This article is cited in 3 scientific papers (total in 3 papers)

The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree

Rustam M. Khakimov

Institute of Mathematics, Do’rmon Yo’li str., 29, Tashkent, 100125, Uzbekistan

Full-text PDF (188 kB) Citations (3)

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Abstract: We consider fertile Hard-Core (HC) models with activity parameter

$\lambda>0$ and four states on the Cayley tree of order two. It is known that there are three types of such models. In this paper for each of these models the uniqueness of the translation-invariant Gibbs measure is proved.

Keywords: Cayley tree, configuration, HC-model, Gibbs measure, translation-invariant measures.

Received: 04.01.2015
Received in revised form: 17.02.2015
Accepted: 06.03.2015

Document Type: Article

UDC: 517.98

Language: English

Citation: Rustam M. Khakimov, “The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 165–172

Citation in format AMSBIB

\Bibitem{Kha15}

\by Rustam~M.~Khakimov

\paper The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree

\jour J. Sib. Fed. Univ. Math. Phys.

\yr 2015

\vol 8

\issue 2

\pages 165--172

\mathnet{http://mi.mathnet.ru/jsfu418}

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https://www.mathnet.ru/eng/jsfu418

https://www.mathnet.ru/eng/jsfu/v8/i2/p165

This publication is cited in the following 3 articles:

R. M. Khakimov, B. Z. Tozhiboev, “Gibbs measures for fertile models with hard-core interactions and four states”, Theoret. and Math. Phys., 219:2 (2024), 823–838
R. M. Khakimov, “Weakly periodic Gibbs measures for HC-models on Cayley trees”, Siberian Math. J., 59:1 (2018), 147–156
R. M. Khakimov, “Gibbs measures for fertile hard-core models on the Cayley tree”, Theoret. and Math. Phys., 186:2 (2016), 294–305

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Журнал Сибирского федерального университета. Серия "Математика и физика"

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Abstract page:	246
Full-text PDF :	86
References:	42

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