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TMF, 2007, Volume 153, Number 1, Pages 86–97 (Mi tmf6123)  

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

Potts model with competing interactions on the Cayley tree: The contour method

G. I. Botirova, U. A. Rozikovb

a National University of Uzbekistan named after M. Ulugbek
b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Potts model with three spin values and with competing interactions of radius $r=2$ on the Cayley tree of order $k=2$. We completely describe the ground states of this model and use the contour method on the tree to prove that this model has three Gibbs measures at sufficiently low temperatures.

Keywords: Cayley tree, configuration, contour method, ground state, Gibbs measure

DOI: https://doi.org/10.4213/tmf6123

Full text: PDF file (451 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 153:1, 1423–1433

Bibliographic databases:

Received: 11.12.2006

Citation: G. I. Botirov, U. A. Rozikov, “Potts model with competing interactions on the Cayley tree: The contour method”, TMF, 153:1 (2007), 86–97; Theoret. and Math. Phys., 153:1 (2007), 1423–1433

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v153/i1/p86

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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. G. I. Botirov, “Periodic Ground States of a Hamiltonian on a Cayley Tree”, Math. Notes, 87:4 (2010), 582–585  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. M. Rakhmatullaev, “Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree”, Theoret. and Math. Phys., 176:3 (2013), 1236–1251  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus
    4. N. M. Khatamov, “New classes of ground states for the Potts model with random competing interactions on a Cayley tree”, Theoret. and Math. Phys., 180:1 (2014), 827–834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. 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
    6. Mukhamedov F., Pah Ch.H., Rahimatullaev M., Jamil H., “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, eds. Rakhimov A., Ural B., Daoud J., Saburov K., Chowdhury M., IOP Publishing Ltd, 2018, UNSP 012021  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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