Translation Invariance of the Periodic Gibbs Measures for the Potts Model on the Cayley Tree

Аннотация

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.