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

In this talk, we consider a $p$-adic Ising model on a Cayley tree of order three. The existence of $G^{(2)}_k$-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.