In this paper we consider a p-adic Ising model on the Cayley tree of order k ≥ 2. We give full description of all p-adic translation-invariant generalized Gibbs measures for k = 3. Moreover, we show the existence of phase transition for p-adic Ising model for any k ≥ 3 when p ≡ 1(mod 4).Mathematics Subject Classification: 37B05, 37B10,12J12, 39A70
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