TRANSLATION-INVARIANT GIBBS MEASURES FOR THE POTTS-SOS MODEL

Authors

  • Raxmatullayev Muzaffar Muxammadjanovich Institute of Mathematics named after V.I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan
  • Rasulova Muhayyo Akbarjon qizi Institute of Mathematics named after V.I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan

DOI:

https://doi.org/10.52754/16948645_2023_1_176

Keywords:

Cayley tree, Potts model, SOS model, Potts-SOS model, Gibbs measures, translation-invariant Gibbs measures.

Abstract

The translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree of order two are described.

References

Rozikov, U. A. Gibbs measures on Cayley trees. [Теxt]/ Rozikov U. A. // World scientific. 2013. DOI: https://doi.org/10.1142/8841

Kuelske, C.. Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree. [Теxt]/ Kuelske C., Rozikov U. A., Khakimov R. M. // Jour. Stat. Phys. – 2014. Том 156. № 1. – С. 189–200. DOI: https://doi.org/10.1007/s10955-014-0986-y

Kuelske, C.Extremality of translation-invariant phases for a three-state SOS-model on the binary tree. [Теxt]/ Kuelske C., Rozikov U. A. // Jour. Stat. Phys. – 2015. Том 160. № 3. – С. 659–680. DOI: https://doi.org/10.1007/s10955-015-1279-9

Saygili, H. Gibbs measures for the Potts-SOS model with three states of spin values. [Теxt]/ Saygili H. // Asian Journal of Current Research. – 2017. Том 1. № 3. – С. 114–121.

Рахматуллаев, М. М. Периодические меры Гиббса для модели Поттса-SOS на дереве Кэли. [Текст]/ Рахматуллаев М. М., Расулова М. А. // Доклады Академии Наук Республики Узбекистан. – 2018. № 1. – С. 15-17.

Расулова, М. А. О периодических мерах гиббса для модели Поттса–SOS на дереве Кэли. [Текст]/ Расулова М. А. // Теоретическая и Математическая Физика. – 2019. Том 199. № 1. – С. 134-141. DOI: https://doi.org/10.4213/tmf9588

Rahmatullaev, M. M. Extremality of translation-invariant Gibbs measures for the Potts-SOS model on the Cayley tree. [Теxt]/ Rahmatullaev M. M., Rasulova M. A. // Journal of Statistical Mechanics: Theory and Experiment. – 2021. № 7. – С. 1-18. DOI: https://doi.org/10.1088/1742-5468/ac08ff

Rasulova, M. A. Periodic Gibbs measures for the three-state Potts-SOS model on a Cayley tree. [Теxt]/ Rasulova M. A. // Uzbek Mathematical Journal. – 2022. Том 66. № 2. – С. 150-155. DOI: https://doi.org/10.29229/uzmj.2022-2-14

Published

2023-06-30

How to Cite

Raxmatullayev, M., & Rasulova , M. (2023). TRANSLATION-INVARIANT GIBBS MEASURES FOR THE POTTS-SOS MODEL. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (1(2), 176–186. https://doi.org/10.52754/16948645_2023_1_176