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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 1, Pages 112–124
DOI: https://doi.org/10.4213/tmf9965 (Mi tmf9965) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
Full-text PDF (590 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf9965
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.
Received: 03.08.2020
Revised: 03.08.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 1, Pages 97–108
DOI: https://doi.org/10.1134/S0040577921010062
Bibliographic databases:
Document Type: Article
Language: Russian
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 $k=3$
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\yr 2021
\vol 206
\issue 1
\pages 112--124
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\crossref{https://doi.org/10.4213/tmf9965}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021TMP...206...97K}
\transl
\jour Theoret. and Math. Phys.
\yr 2021
\vol 206
\issue 1
\pages 97--108
\crossref{https://doi.org/10.1134/S0040577921010062}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000664262800006}
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  • https://www.mathnet.ru/eng/tmf9965
  • https://doi.org/10.4213/tmf9965
  • https://www.mathnet.ru/eng/tmf/v206/i1/p112
    • This publication is cited in the following 4 articles:
    1. B. Z. Tozhiboev, R. M. Khakimov, “Mery Gibbsa dlya $\mathrm{HC}$-modeli v sluchae grafa tipa “klyuch” na dereve Keli”, Matem. zametki, 117:4 (2025), 575–590  mathnet  crossref
    2. 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  mathnet  crossref  crossref  mathscinet  adsnasa
    3. Rustamjon Khakimov, Muhtorjon Makhammadaliev, Kamola Umirzakova, “Alternative Gibbs measure for fertile three-state Hard-Core models on a Cayley tree”, Phase Transitions, 2024, 1  crossref
    4. F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the $\lambda$-model on the binary Cayley tree”, Theoret. and Math. Phys., 210:3 (2022), 411–424  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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