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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 1, Pages 86–97
DOI: https://doi.org/10.4213/tmf6123 (Mi tmf6123) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Potts model with competing interactions on the Cayley tree: The contour method

G. I. Botirova, U. A. Rozikovb

a National University of Uzbekistan named after M. Ulugbek
b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Full-text PDF (451 kB) Citations (22)
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DOI: https://doi.org/10.4213/tmf6123
Abstract: We consider the Potts model with three spin values and with competing interactions of radius $r=2$ on the Cayley tree of order $k=2$. We completely describe the ground states of this model and use the contour method on the tree to prove that this model has three Gibbs measures at sufficiently low temperatures.
Keywords: Cayley tree, configuration, contour method, ground state, Gibbs measure.
Received: 11.12.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 1, Pages 1423–1433
DOI: https://doi.org/10.1007/s11232-007-0125-x
Bibliographic databases:
Language: Russian
Citation: G. I. Botirov, U. A. Rozikov, “Potts model with competing interactions on the Cayley tree: The contour method”, TMF, 153:1 (2007), 86–97; Theoret. and Math. Phys., 153:1 (2007), 1423–1433
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v153/i1/p86
    • This publication is cited in the following 22 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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