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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 2, Pages 258–279
DOI: https://doi.org/10.4213/tmf9818 (Mi tmf9818) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model

R. M. Khakimova, M. T. Makhammadalievb

a Namangan Department, Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Namangan, Uzbekistan
b Namangan State University, Namangan, Uzbekistan
Full-text PDF (515 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf9818
Abstract: We study a "hard-core" model on a Cayley tree. In the case of a normal divisor of index 4, we show the uniqueness of weakly periodic Gibbs measures under certain conditions on the parameters. Moreover, we prove that there exist weakly periodic (nonperiodic) Gibbs measures different from those previously known.
Keywords: Cayley tree, configuration, hard-core model, Gibbs measure, translation-invariant measure, periodic measure, weakly periodic measure.
Received: 12.09.2019
Revised: 23.02.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 2, Pages 1059–1078
DOI: https://doi.org/10.1134/S0040577920080073
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. M. Khakimov, M. T. Makhammadaliev, “Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model”, TMF, 204:2 (2020), 258–279; Theoret. and Math. Phys., 204:2 (2020), 1059–1078
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9818
  • https://www.mathnet.ru/eng/tmf/v204/i2/p258
    • This publication is cited in the following 8 articles:
    1. U. A. Rozikov, R. M. Khakimov, M. T. Makhammadaliev, “Gibbs measures for a Hard-Core model with a countable set of states”, Rev. Math. Phys., 37:04 (2025)  crossref
    2. Muhtorjon Makhammadaliev, “Weakly periodic gibbs measures for the HC model with a countable set of spin values”, Reports on Mathematical Physics, 94:1 (2024), 83  crossref
    3. R. M. Khakimov, M. T. Makhammadaliev, “Translation-Invariant Gibbs Measures for the Hard Core Model with a Countable Set of Spin Values”, Lobachevskii J Math, 45:8 (2024), 3897  crossref
    4. 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), 2350024  crossref  mathscinet
    5. R. M. Khakimov, M. T. Makhammadaliev, U. A. Rozikov, “Gibbs measures for HC-model with a countable set of spin values on a Cayley tree”, Math. Phys. Anal. Geom., 26:2 (2023), 9  crossref
    6. U. A. Rozikov, F. H. Haydarov, “A HC model with countable set of spin values: Uncountable set of Gibbs measures”, Rev. Math. Phys., 35:01 (2023), 2250039  crossref  mathscinet
    7. N. N. Ganikhodzhaev, U. A. Rozikov, N. M. Khatamov, “Gibbs measures for the HC Blume–Capel model with countably many states on a Cayley tree”, Theoret. and Math. Phys., 211:3 (2022), 856–865  mathnet  crossref  crossref  mathscinet  adsnasa
    8. R. M. Khakimov, M. T. Makhammadaliev, “Nonprobability Gibbs measures for the HC model with a countable set of spin values for a “wand”-type graph on a Cayley tree”, Theoret. and Math. Phys., 212:3 (2022), 1259–1275  mathnet  crossref  crossref  mathscinet  adsnasa
    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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