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TMF, 2014, Volume 179, Number 1, Pages 24–35 (Mi tmf8599)  

This article is cited in 1 scientific paper (total in 1 paper)

Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree

R. M. Khakimov

Namangam State University

Abstract: We study Potts and “solid-on-solid” models with $q\ge2$ states on the Cayley tree of order $k\ge1$. For any values of the parameter $q$ in the Potts model and $q\le6$ in the “solid-on-solid” model, we find sets containing all translation-invariant Gibbs measures.

Keywords: Cayley tree, configuration, Gibbs measure, Potts model, “solid-on-solid” model, periodic measure, translation-invariant measure

DOI: https://doi.org/10.4213/tmf8599

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English version:
Theoretical and Mathematical Physics, 2014, 179:1, 405–415

Bibliographic databases:

Received: 02.10.2013

Citation: R. M. Khakimov, “Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree”, TMF, 179:1 (2014), 24–35; Theoret. and Math. Phys., 179:1 (2014), 405–415

Citation in format AMSBIB
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\paper Localization of translation-invariant Gibbs measures for the~Potts and ``solid-on-solid'' models on a~Cayley tree
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Haydarov F. Khakimov R., “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, ed. Ayupov S. Chilin V. Ganikhodjaev N. Mukhamedov F. Rakhimov I., IOP Publishing Ltd, 2016, 012019  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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