On three-state Potts model on a Cayley tree: periodic measures
  In this paper we show that under some conditions on the parameter of the Potts model with three states with zero external field on the Cayley tree of order $k>2$, there are exactly two periodic (non translation-invariant) Gibbs measures. 
F. H. Haydarov, R. M. Khakimov
math-ph math.MP