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TMF, 2021, Volume 206, Number 1, Pages 112–124 (Mi tmf9965)  

Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order $k=3$

R. M. Khakimova*, K. O. Umirzakovab

a Namangan Department, Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Namangan, Uzbekistan
b Namangam State University, , Namangan, Uzbekistan

Abstract: We study fertile hard-core models with three states and an activity parameter $\lambda>0$ on the Cayley tree of order $k=3$. It is known that there are four types of such models. For two of them, we find the regions where the unique translation-invariant Gibbs measure is (not) extremal. For one of the considered models, we find the conditions under which the extremal measure is not unique.

Keywords: Cayley tree, configuration, hard-core model, fertile graph, Gibbs measure, translation-invariant measure, measure extremality.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9965

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English version:
Theoretical and Mathematical Physics, 2021, 206:1, 97–108

Bibliographic databases:

Received: 03.08.2020
Revised: 03.08.2020

Citation: R. M. Khakimov, K. O. Umirzakova, “Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order $k=3$”, TMF, 206:1 (2021), 112–124; Theoret. and Math. Phys., 206:1 (2021), 97–108

Citation in format AMSBIB
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\by R.~M.~Khakimov, K.~O.~Umirzakova
\paper Extremality of the~unique translation-invariant Gibbs measure for hard-core models on the~Cayley tree of order $k=3$
\jour TMF
\yr 2021
\vol 206
\issue 1
\pages 112--124
\mathnet{http://mi.mathnet.ru/tmf9965}
\crossref{https://doi.org/10.4213/tmf9965}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4224000}
\transl
\jour Theoret. and Math. Phys.
\yr 2021
\vol 206
\issue 1
\pages 97--108
\crossref{https://doi.org/10.1134/S0040577921010062}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000664262800006}


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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