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TMF, 2016, Volume 189, Number 2, Pages 286–295 (Mi tmf9138)  

This article is cited in 2 scientific papers (total in 2 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

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

DOI: https://doi.org/10.4213/tmf9138

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English version:
Theoretical and Mathematical Physics, 2016, 189:2, 1651–1659

Bibliographic databases:

Received: 22.12.2015

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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\paper Translation-invariant and periodic Gibbs measures for the~Potts model on a~Cayley tree
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\vol 189
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\pages 286--295
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\jour Theoret. and Math. Phys.
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\vol 189
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\pages 1651--1659
\crossref{https://doi.org/10.1134/S004057791611009X}
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  • http://mi.mathnet.ru/eng/tmf9138
  • https://doi.org/10.4213/tmf9138
  • http://mi.mathnet.ru/eng/tmf/v189/i2/p286

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058  mathnet  crossref  crossref  adsnasa  isi  elib
    2. R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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