On Phase Transitions for $P$-Adic Potts Model with Competing   Interactions on a Cayley Tree
  In the paper we considere three state $p$-adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the $p$-adic Gibbs measures to the solution of certain recursive equation, and using it we will prove that a phase transition occurs if and only if $p=3$ for any value (non zero) of interactions. As well, we completely solve the uniqueness problem for the considered model in a $p$-adic context. Namely, if $p\neq 3$ then there is only a unique Gibbs measure the model. 
Farrukh Mukhamedov, Utkir Rozikov, Jose Fernando F. Mendes