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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 1, Pages 156–176
DOI: https://doi.org/10.4213/tmf10158 (Mi tmf10158) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree

U. A. Rozikovabc, M. M. Rahmatullaevad, R. M. Khakimovad

a V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan
b Akfa University, Tashkent, Uzbekistan
c National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan
d Namangam State University, Namangam, Uzbekistan
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DOI: https://doi.org/10.4213/tmf10158
Abstract: We study the Potts model in translation-invariant and periodic external fields on the Cayley tree of order $k\geq 2$. For the Potts model in a translation-invariant external field for $k\geq 2$, the nonuniqueness of the translation-invariant and periodic Gibbs measure is shown. It is proved that for the Potts model in an external field that is not translation-invariant, translation-invariant Gibbs measures do not exist on the Cayley tree of order $k\geq 2$. Periodic Gibbs measures are also studied for the Potts model in a periodic external field. We prove that under certain conditions, the number of such measures can be at least three.
Keywords: Cayley tree, Gibbs measure, Potts model, periodic external field, translation-invariant external field.
Received: 05.08.2021
Revised: 24.09.2021
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 1, Pages 135–153
DOI: https://doi.org/10.1134/S004057792201010X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: U. A. Rozikov, M. M. Rahmatullaev, R. M. Khakimov, “Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree”, TMF, 210:1 (2022), 156–176; Theoret. and Math. Phys., 210:1 (2022), 135–153
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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