Translation Invariance of the Periodic Gibbs Measures for the Potts Model on the Cayley Tree
R. M. KhakimovNamangan State University, Namangan, UzbekistanM. T. MakhammadalievNamangan State University, Namangan, Uzbekistan
ABI
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 kth-order Cayley tree, we show that all periodic Gibbs measures are translation-invariant for all parameter values.