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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 2, Pages 286–295
DOI: https://doi.org/10.4213/tmf9138 (Mi tmf9138) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree

R. M. Khakimova, F. Kh. Khaidarovb

a Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
b Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
Full-text PDF (434 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf9138
Abstract: We study translation-invariant Gibbs measures on a Cayley tree of order $k=3$ for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order $k$ for the antiferromagnetic $q$-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order $k\ge3$ that are defined on some invariant sets.
Keywords: Cayley tree, configuration, Potts model, Gibbs measure, translation-invariant measure, periodic measure.
Received: 22.12.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 2, Pages 1651–1659
DOI: https://doi.org/10.1134/S004057791611009X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, TMF, 189:2 (2016), 286–295; Theoret. and Math. Phys., 189:2 (2016), 1651–1659
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v189/i2/p286
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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