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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 1, Pages 60–70
DOI: https://doi.org/10.4213/tmf6966 (Mi tmf6966) 		 
This article is cited in 7 scientific papers (total in 7 papers)

The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model

U. A. Rozikova, R. M. Khakimovb

a Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
b Namangan State University, Namangan, Uzbekistan
Full-text PDF (411 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf6966
Abstract: We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant.
Keywords: Cayley tree, configuration, hard-core model, Gibbs measure, periodic measure, weakly periodic measure.
Received: 20.02.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 1, Pages 1377–1386
DOI: https://doi.org/10.1007/s11232-012-0120-8
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: U. A. Rozikov, R. M. Khakimov, “The uniqueness condition for a weakly periodic Gibbs measure for the hard-core model”, TMF, 173:1 (2012), 60–70; Theoret. and Math. Phys., 173:1 (2012), 1377–1386
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6966
  • https://doi.org/10.4213/tmf6966
  • https://www.mathnet.ru/eng/tmf/v173/i1/p60
    • This publication is cited in the following 7 articles:
    1. 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  crossref
    2. 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  mathnet  crossref  mathscinet
    3. 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  mathnet  crossref  crossref  adsnasa  isi  elib
    4. R. M. Khakimov, “Weakly periodic Gibbs measures for HC-models on Cayley trees”, Siberian Math. J., 59:1 (2018), 147–156  mathnet  crossref  crossref  isi  elib
    5. R. M. Khakimov, “Gibbs measures for fertile hard-core models on the Cayley tree”, Theoret. and Math. Phys., 186:2 (2016), 294–305  mathnet  crossref  crossref  mathscinet  isi  elib
    6. R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 189:2 (2016), 1651–1659  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. R. M. Khakimov, “Weakly Periodic Gibbs Measures in the HC-Model for a Normal Divisor of Index Four”, Ukr Math J, 67:10 (2016), 1584  crossref
    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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