\(\boldsymbol{H}_{\boldsymbol{A}}\)-Weakly Periodic \(\boldsymbol{p}\)-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 \(H_{A}\) -weakly periodic (non-periodic) \(p\) -adic generalized Gibbs measures of this model is investigated. Moreover, the boundedness of such kinds of measures are established, which yields the occurrence of a phase transition.