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

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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

$2$ -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

$4$ -state HC-models with the activity parameter

λ > 0

$\lambda>0$ . 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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Linking options:

https://www.mathnet.ru/eng/smj2964

https://www.mathnet.ru/eng/smj/v59/i1/p185

This publication is cited in the following 8 articles:

N. M. Khatamov, “Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree”, Math. Notes, 115:1 (2024), 89–101
U. A. Rozikov, R. M. Khakimov, M. T. Makhammadaliev, “Gibbs Periodic Measures for a Two-State HC-Model on a Cayley Tree”, J Math Sci, 278:4 (2024), 647
R. M. Khakimov, M. T. Makhammadaliev, F. H. Haydarov, “New class of Gibbs measures for two-state hard-core model on a Cayley tree”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 26:04 (2023)
N. M. Khatamov, “Extremality of Gibbs Measures for the $HC$ -Blume–Capel Model on the Cayley Tree”, Math. Notes, 111:5 (2022), 768–781
U. A. Rozikov, R. M. Khakimov, M. T. Makhammadaliev, “Periodicheskie mery Gibbsa dlya NS-modeli s dvumya sostoyaniyami na dereve Keli”, Nauka — tekhnologiya — obrazovanie — matematika — meditsina, SMFN, 68, no. 1, Rossiiskii universitet druzhby narodov, M., 2022, 95–109
N. M. Khatamov, “Ekstremalnost nekotorykh mer Gibbsa dlya HC-modeli Blyuma-Kapelya na dereve Keli”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 256–277
N. M. Khatamov, “Periodic Gibbs Measures and Their Extremes for the HC–Blume–Capel Model in the Case of a "Wand" on the Cayley Tree”, Lobachevskii J Math, 43:9 (2022), 2515
R. M. Khakimov, M. T. Makhammadaliev, “Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model”, Theoret. and Math. Phys., 204:2 (2020), 1059–1078

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

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