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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 2, Pages 311–322
DOI: https://doi.org/10.4213/tmf6642 (Mi tmf6642) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Nonuniqueness of a Gibbs measure for a model on the Cayley tree

U. A. Rozikov, G. T. Madgoziev

Institute of Mathematics and Information Technologies, Uzbek Academy of Sciences, Tashkent, Uzbekistan
Full-text PDF (434 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf6642
Abstract: We propose a model on the Cayley tree and prove that a uncountable set of ˆG-periodic Gibbs measures exists for this model, in contrast to models studied previously.
Keywords: Cayley tree, configuration, hard-core model, Gibbs measure.
Received: 11.10.2010
Revised: 29.11.2010
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 2, Pages 668–679
DOI: https://doi.org/10.1007/s11232-011-0051-9
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: U. A. Rozikov, G. T. Madgoziev, “Nonuniqueness of a Gibbs measure for a model on the Cayley tree”, TMF, 167:2 (2011), 311–322; Theoret. and Math. Phys., 167:2 (2011), 668–679
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6642
  • https://doi.org/10.4213/tmf6642
  • https://www.mathnet.ru/eng/tmf/v167/i2/p311
    • This publication is cited in the following 3 articles:
    1. N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 836–845  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. N. M. Khatamov, “Nonuniqueness of a Gibbs measure for the Ising ball model”, Theoret. and Math. Phys., 180:3 (2014), 1030–1039  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    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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    References:85
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