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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 153, Number 1, Pages 86–97
DOI: https://doi.org/10.4213/tmf6123
(Mi tmf6123)
 

This article is cited in 23 scientific papers (total in 23 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
References:
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.
Received: 11.12.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 153, Issue 1, Pages 1423–1433
DOI: https://doi.org/10.1007/s11232-007-0125-x
Bibliographic databases:
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/tmf6123
  • https://doi.org/10.4213/tmf6123
  • https://www.mathnet.ru/eng/tmf/v153/i1/p86
  • This publication is cited in the following 23 articles:
    1. Begzod Isakov, Olimkhon Akhmedov, “FUNKTsIONALNYE URAVNENIYa DLYa PREDELNYKh MER GIBBSA MODELI IZINGA-POTTSA NA DEREVE KELI”, VOGUMFT, 2024, no. 1(4), 90  crossref
    2. M. M. Rahmatullaev, M. A. Rasulova, “Ground States and Gibbs Measures for the Potts-SOS Model with an External Field on the Cayley Tree”, Lobachevskii J Math, 45:1 (2024), 518  crossref
    3. Muhayyo A. Rasulova, “Ground states for the potts model with an external field”, Reports on Mathematical Physics, 94:3 (2024), 325  crossref
    4. G. I. Botirov, Z. E. Mustafoeva, “Gibbs measures for the Potts model with a countable set of spin values on a Cayley tree”, Theoret. and Math. Phys., 214:2 (2023), 273–281  mathnet  crossref  crossref  mathscinet  adsnasa
    5. M. M. Rahmatullaev, B. M. Isakov, “Ground states of Ising-Potts model on Cayley tree”, Ufa Math. J., 15:1 (2023), 43–55  mathnet  crossref
    6. M. M. Rakhmatullaev, M. A. Rasulova, “Opisanie slabo periodicheskikh osnovnykh sostoyanii dlya modeli Pottsa s vneshnim polem i schetnym mnozhestvom znachenii spina na dereve Keli”, Vladikavk. matem. zhurn., 25:4 (2023), 103–119  mathnet  crossref
    7. G. Botirov, F. Haydarov, U. Qayumov, “Gibbs Measures of the Blume–Emery–Griffiths Model on the Cayley Tree”, Math Phys Anal Geom, 26:1 (2023)  crossref
    8. Muzaffar M. Rahmatullaev, Muhayyo A. Rasulova, Javohir N. Asqarov, “Ground States and Gibbs Measures of Ising Model with Competing Interactions and an External Field on a Cayley Tree”, J Stat Phys, 190:7 (2023)  crossref
    9. Muzaffar M. Rahmatullaev, Bunyod U. Abraev, “On ground states for the SOS model with competing interactions”, Zhurn. SFU. Ser. Matem. i fiz., 15:2 (2022), 162–175  mathnet  crossref  mathscinet
    10. F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the $\lambda$-model on the binary Cayley tree”, Theoret. and Math. Phys., 210:3 (2022), 411–424  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    11. M. M. Rahmatullaev, M. A. Rasulova, “Periodic Ground States for the Potts Model with External Field and a Countable Set of Spin Values on the Cayley Tree”, Math. Notes, 112:1 (2022), 116–125  mathnet  crossref  crossref  mathscinet
    12. G. I. Botirov, U. U. Qayumov, “Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree”, Theoret. and Math. Phys., 209:2 (2021), 1633–1642  mathnet  crossref  crossref  adsnasa  isi  elib
    13. Rozikov U.A., “Gibbs Measures of Potts Model on Cayley Trees: a Survey and Applications”, Rev. Math. Phys., 33:10 (2021), 2130007  crossref  mathscinet  isi
    14. Mukhamedov F.M., Rakhmatullaev M.M., Rasulova M.A., “Weakly Periodic Ground States For the Lambda-Model”, Ukr. Math. J., 72:5 (2020), 771–784  crossref  mathscinet  isi
    15. Mukhamedov F., Pah Ch.H., Jamil H., Rahmatullaev M., “On Ground States and Phase Transition For Lambda-Model With the Competing Potts Interactions on Cayley Trees”, Physica A, 549 (2020), 124184  crossref  mathscinet  isi
    16. Farrukh M. Mukhamedov, Muzaffar M. Rahmatullaev, M. A. Rasulova, “Slabo periodicheskie osnovnye sostoyaniya dlya λ-modeli”, Ukr. Mat. Zhurn., 72:5 (2020)  crossref
    17. 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
    18. G. I. Botirov, M. M. Rahmatullaev, Springer Proceedings in Mathematics & Statistics, 264, Algebra, Complex Analysis, and Pluripotential Theory, 2018, 59  crossref
    19. 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
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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