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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 1, Pages 24–35
DOI: https://doi.org/10.4213/tmf8599 (Mi tmf8599) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

R. M. Khakimov

Namangam State University
Full-text PDF (414 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf8599
Abstract: We study Potts and “solid-on-solid” models with q⩾2 states on the Cayley tree of order k⩾1. For any values of the parameter q in the Potts model and q⩽6 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.
Received: 02.10.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 1, Pages 405–415
DOI: https://doi.org/10.1007/s11232-014-0152-3
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf8599
  • https://doi.org/10.4213/tmf8599
  • https://www.mathnet.ru/eng/tmf/v179/i1/p24
    • This publication is cited in the following 3 articles:
    1. O. Sh. Karshiboev, “Periodic Gibbs measures for the three-state SOS model on a Cayley tree with a translation-invariant external field”, Theoret. and Math. Phys., 212:3 (2022), 1276–1283  mathnet  crossref  crossref  mathscinet  adsnasa
    2. Muzaffar M. Rahmatullaev, Obid Sh. Karshiboev, “Gibbs measures for the three-state SOS model with external field on a Cayley tree”, Positivity, 26:5 (2022)  crossref
    3. 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
    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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    Abstract page:337
    Full-text PDF :172
    References:67
    First page:25
     
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