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TMF, 2013, Volume 176, Number 3, Pages 513–528 (Mi tmf8522)  

This article is cited in 5 scientific papers (total in 5 papers)

The $p$-adic Potts model on the Cayley tree of order three

F. M. Mukhamedova, H. Akinb

a Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Pahang, Malaysia
b Faculty of Education, Zirve University, Gaziantep, Turkey

Abstract: We study a phase transition problem for the $q$-state $p$-adic Potts model on the Cayley tree of order three. We find certain conditions for the existence of $p$-adic Gibbs measures and then establish the existence of a phase transition.

Keywords: $p$-adic number, Potts model, $p$-adic quasi-Gibbs measure, phase transition

DOI: https://doi.org/10.4213/tmf8522

Full text: PDF file (513 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 176:3, 1267–1279

Bibliographic databases:

MSC: 46S10, 82B26, 12J12, 39A70, 47H10, 60K35
Received: 17.02.2013

Citation: F. M. Mukhamedov, H. Akin, “The $p$-adic Potts model on the Cayley tree of order three”, TMF, 176:3 (2013), 513–528; Theoret. and Math. Phys., 176:3 (2013), 1267–1279

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  • https://doi.org/10.4213/tmf8522
  • http://mi.mathnet.ru/eng/tmf/v176/i3/p513

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. F. Mukhamedov, “On the strong phase transition for the one-dimensional countable state $p$-adic Potts model”, J. Stat. Mech.-Theory Exp., 2014, P01007  crossref  mathscinet  isi  elib  scopus
    2. F. Mukhamedov, “Renormalization method in $p$-adic $\lambda$-model on the Cayley tree”, Int. J. Theor. Phys., 54:10 (2015), 3577–3595  crossref  mathscinet  zmath  isi  elib  scopus
    3. F. M. Mukhamedov, M. Kh. Saburov, O. N. Khakimov, “Translation-invariant $p$-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree”, Theoret. and Math. Phys., 187:1 (2016), 583–602  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. F. Mukhamedov, O. Khakimov, “_orig phase transition and chaos: p-adic potts model on a cayley tree”, Chaos Solitons Fractals, 87 (2016), 190–196  crossref  mathscinet  zmath  isi  elib  scopus
    5. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “$p$-Adic mathematical physics: the first 30 years”, $p$-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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