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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 214, Number 3, Pages 469–485
DOI: https://doi.org/10.4213/tmf10376 (Mi tmf10376) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The description of generalized translation-invariant $p$-adic Gibbs measures for the Potts model on the Cayley tree of order three

M. Alpa, Chin Hee Pahb, M. K. Saburova

a College of Engineering and Technology, American University of the Middle East, Kuwait City, Kuwait
b Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, Kuantan, Malaysia
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DOI: https://doi.org/10.4213/tmf10376
Abstract: We describe generalized translation-invariant $p$-adic Gibbs measures for the Potts model on the Cayley tree of order three, confirming and extending the related results in the literature. We introduce a cube root function over the $p$-adic field $\mathbb{Q}_p$, which enables us to explicitly prescribe all roots of the cubic monomial equation over $\mathbb{Q}_p$.
Keywords: Gibbs measure, Potts model, Cayley tree, $p$-adic field.
Received: 18.09.2022
Revised: 15.10.2022
English version:
Theoretical and Mathematical Physics, 2023, Volume 214, Issue 3, Pages 406–420
DOI: https://doi.org/10.1134/S0040577923030066
Bibliographic databases:
Document Type: Article
MSC: 82B26, 46S10, 12J12, 39A70, 47H10, 60K35
Language: Russian
Citation: M. Alp, Chin Hee Pah, M. K. Saburov, “The description of generalized translation-invariant $p$-adic Gibbs measures for the Potts model on the Cayley tree of order three”, TMF, 214:3 (2023), 469–485; Theoret. and Math. Phys., 214:3 (2023), 406–420
Citation in format AMSBIB
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\by M.~Alp, Chin~Hee~Pah, M.~K.~Saburov
\paper The~description of generalized translation-invariant $p$-adic
Gibbs measures for the~Potts model on the~Cayley tree of order
three
\jour TMF
\yr 2023
\vol 214
\issue 3
\pages 469--485
\mathnet{http://mi.mathnet.ru/tmf10376}
\crossref{https://doi.org/10.4213/tmf10376}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563417}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...214..406A}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 214
\issue 3
\pages 406--420
\crossref{https://doi.org/10.1134/S0040577923030066}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85160054942}
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  • https://www.mathnet.ru/eng/tmf10376
  • https://doi.org/10.4213/tmf10376
  • https://www.mathnet.ru/eng/tmf/v214/i3/p469
    • This publication is cited in the following 1 articles:
    1. M. A. K. Ahmad, M. Alp, O. Kozhushkina, J. Long, M. Saburov, J. Trulen, “Trees and Solvability of Depressed Cubics over $\mathbb{Q}_{2}$”, P-Adic Num Ultrametr Anal Appl, 17:1 (2025), 85  crossref
    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:182
    Full-text PDF :55
    Russian version HTML:102
    References:45
    First page:2
     
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