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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 1, Pages 117–134
DOI: https://doi.org/10.4213/tmf9448 (Mi tmf9448) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree

U. A. Rozikova, R. M. Khakimovb, F. Kh. Khaidarovc

a Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
b Namangam State University, Namangan, Uzbekistan
c Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan
Full-text PDF (753 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf9448
Abstract: We study translation-invariant Gibbs measures for the ferromagnetic Potts model with $q$ states on the Cayley tree of order $k$ and generalize some earlier results. We consider the question of the extremality of the known translation-invariant Gibbs measures for the Potts model with three states on the Cayley tree of order $k=3$.
Keywords: Cayley tree, configuration, Potts model, Gibbs measure, translation-invariant measure, measure extremality.
Received: 17.08.2017
Revised: 11.10.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 1, Pages 1043–1058
DOI: https://doi.org/10.1134/S0040577918070103
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, TMF, 196:1 (2018), 117–134; Theoret. and Math. Phys., 196:1 (2018), 1043–1058
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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