$$\boldsymbol{H}_{\boldsymbol{A}}$$-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.

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