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TMF, 2013, Volume 175, Number 2, Pages 300–312 (Mi tmf8423)  

This article is cited in 12 scientific papers (total in 12 papers)

Periodic Gibbs measures for the Potts model on the Cayley tree

U. A. Rozikova, R. M. Khakimovb

a Institute of Mathematics, Tashkent, Uzbekistan
b Namangan State University, Namangan, Uzbekistan

Abstract: We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic measure, translation-invariant measure

DOI: https://doi.org/10.4213/tmf8423

Full text: PDF file (444 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 175:2, 699–709

Bibliographic databases:

Received: 08.10.2012
Revised: 26.12.2012

Citation: U. A. Rozikov, R. M. Khakimov, “Periodic Gibbs measures for the Potts model on the Cayley tree”, TMF, 175:2 (2013), 300–312; Theoret. and Math. Phys., 175:2 (2013), 699–709

Citation in format AMSBIB
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\paper Periodic Gibbs measures for the~Potts model on the~Cayley tree
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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. R. M. Khakimov, “Localization of translation-invariant Gibbs measures for the Potts and “solid-on-solid” models on a Cayley tree”, Theoret. and Math. Phys., 179:1 (2014), 405–415  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Rustamjon M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, Zhurn. SFU. Ser. Matem. i fiz., 7:3 (2014), 297–304  mathnet
    3. 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
    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. Haydarov F. Khakimov R., “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, ed. Ayupov S. Chilin V. Ganikhodjaev N. Mukhamedov F. Rakhimov I., IOP Publishing Ltd, 2016, 012019  crossref  mathscinet  isi  scopus
    6. 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
    7. F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the $\lambda$ model on the Cayley tree”, Theoret. and Math. Phys., 194:2 (2018), 260–273  mathnet  crossref  crossref  adsnasa  isi  elib
    8. F. Mukhamedov, Ch. H. Pah, M. Rahimatullaev, H. Jamil, “Periodic and weakly periodic ground states for the $\lambda$-model on Cayley tree”, 4th International Conference on Mathematical Applications in Engineering 2017 (ICMAE'17), Journal of Physics Conference Series, 949, ed. A. Rakhimov, B. Ural, J. Daoud, K. Saburov, M. Chowdhury, IOP Publishing Ltd, 2018, UNSP 012021  crossref  isi  scopus
    9. L. Ahmad Mohd Ali Khameini Liao, M. Saburov, “Periodic $p$-adic Gibbs measures of $q$-state Potts model on Cayley trees I: the chaos implies the vastness of the set of $p$-adic Gibbs measures”, J. Stat. Phys., 171:6 (2018), 1000–1034  crossref  mathscinet  zmath  isi  scopus
    10. U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058  mathnet  crossref  crossref  adsnasa  isi  elib
    11. 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
    12. R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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