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TMF, 2014, Volume 180, Number 3, Pages 307–317 (Mi tmf8647)  

This article is cited in 6 scientific papers (total in 6 papers)

The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree

M. M. Rakhmatullaev

Institute for Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study the $q$-state Potts model on a Cayley tree of order $k\ge2$. In the group representation of the Cayley tree for the ferromagnetic Potts model, we single out a set of index-$2$ subgroups under which each weakly periodic Gibbs measure is translation invariant. For the anti-ferromagnetic Potts model with $k\ge2$ and $q\ge 2$, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.

Keywords: Cayley tree, Gibbs measure, Potts model, weakly periodic Gibbs measure

DOI: https://doi.org/10.4213/tmf8647

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English version:
Theoretical and Mathematical Physics, 2014, 180:3, 1019–1029

Bibliographic databases:

Received: 01.02.2014

Citation: M. M. Rakhmatullaev, “The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree”, TMF, 180:3 (2014), 307–317; Theoret. and Math. Phys., 180:3 (2014), 1019–1029

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v180/i3/p307

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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. M. M. Rahmatullaev, “A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree”, Siberian Math. J., 56:5 (2015), 929–935  mathnet  crossref  crossref  isi  elib
    2. M. M. Rahmatullaev, “On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree”, Zhurn. matem. fiz., anal., geom., 12:4 (2016), 302–314  mathnet  crossref  mathscinet
    3. Rakhmatullaev M.M., “On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree”, Ukr. Math. J., 68:4 (2016), 598–611  crossref  mathscinet  isi  scopus
    4. Mukhamedov F. Khakimov O., “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. U. A. Rozikov, M. M. Rakhmatullaev, “Free energies of the Potts model on a Cayley tree”, Theoret. and Math. Phys., 190:1 (2017), 98–108  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. M. A. Rasulova, “Periodic Gibbs measures for the Potts–SOS model on a Cayley tree”, Theoret. and Math. Phys., 199:1 (2019), 586–592  mathnet  crossref  crossref  adsnasa  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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