On periodic p-adic generalized Gibbs measures for Ising model on a Cayley tree

In the present paper, we consider a p-adic Ising model on a Cayley tree of order three. The existence of $$G_k^{(2)}$$ -periodic non-translation-invariant p-adic generalized Gibbs measures of this model is investigated. Moreover, the boundedness of such kinds of measures is established, which yields the occurrence of a phase transition.