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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 199, Number 2, Pages 291–301
DOI: https://doi.org/10.4213/tmf9574 (Mi tmf9574) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree

R. M. Khakimov, M. T. Makhammadaliev

Namangam State University, Namangan, Uzbekistan
Full-text PDF (409 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf9574
Abstract: We study the Potts model with a zero external field on the Cayley tree. For the antiferromagnetic Potts model with $q$ states on a second-order Cayley tree and for the ferromagnetic Potts model with $q$ states on a $k$th-order Cayley tree, we show that all periodic Gibbs measures are translation-invariant for all parameter values.
Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic measure, translation-invariant measure.
Received: 11.03.2018
Revised: 24.10.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 199, Issue 2, Pages 726–735
DOI: https://doi.org/10.1134/S004057791905009X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, TMF, 199:2 (2019), 291–301; Theoret. and Math. Phys., 199:2 (2019), 726–735
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    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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