On constructive description of Gibbs measures for the Potts model on a Cayley tree

  • M. Rahmatullaev Namangan state university
  • F. К. Rafikov Uzbekistan
  • Sh. Kh. Azamov Коканд. держ. пед. iн-т, Узбекистан
Keywords: Cayley tree

Abstract

UDC 517.9

We consider the Potts model on a Cayley tree and prove the existence of Gibbs measures built by using the method suggested in [H. Akin, U. A. Rozikov, S. Temir, A new set of limiting Gibbs measures for the Ising model on a Cayley tree, J. Stat. Phys., 142, № 2, 314 – 321 (2011)]. In addition, we prove that there exist $(k_0)$-translation invariant Gibbs measures for the Potts model on a Cayley tree and calculate the free energy of these Gibbs measures.

Author Biography

Sh. Kh. Azamov , Коканд. держ. пед. iн-т, Узбекистан

 

 

 

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Published
20.07.2021
How to Cite
Rahmatullaev, M., Rafikov F. К., and S. K. Azamov. “On Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 7, July 2021, pp. 938 -50, doi:10.37863/umzh.v73i7.6408.
Section
Research articles