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TMF, 2013, Volume 176, Number 3, Pages 477–493 (Mi tmf8530)  

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

Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree

M. M. Rakhmatullaev

Namangant State University, Uzbekistan

Abstract: For the Potts model with competing interactions, we describe the set of weakly periodic ground states corresponding to index-two normal divisors of the Cayley tree group representation. We also study some weakly periodic Gibbs measures.

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

DOI: https://doi.org/10.4213/tmf8530

Full text: PDF file (424 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 176:3, 1236–1251

Bibliographic databases:

Received: 11.03.2013

Citation: M. M. Rakhmatullaev, “Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree”, TMF, 176:3 (2013), 477–493; Theoret. and Math. Phys., 176:3 (2013), 1236–1251

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8530
  • http://mi.mathnet.ru/eng/tmf/v176/i3/p477

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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. Rakhmatullaev, “The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 180:3 (2014), 1019–1029  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 836–845  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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. M. A. Rasulova, M. M. Rahmatullaev, “Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree”, Siberian Adv. Math., 26:3 (2016), 215–229  mathnet  crossref  crossref  mathscinet  elib
    5. 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
    6. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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