This article is cited in 8 papers

Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree

R. M. Khakimov, M. T. Makhammadaliev

Namangam State University, Namangan, Uzbekistan

Abstract: We study the Potts model with a zero external field on the Cayley tree. For the antiferromagnetic Potts model with $q$ states on a second-order Cayley tree and for the ferromagnetic Potts model with $q$ states on a $k$th-order Cayley tree, we show that all periodic Gibbs measures are translation-invariant for all parameter values.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic measure, translation-invariant measure.

Received: 11.03.2018
Revised: 24.10.2018

DOI: 10.4213/tmf9574

 English version: Theoretical and Mathematical Physics, 2019, 199:2, 726–735

Bibliographic databases:

• 
• 
• 
• 
•