On HA-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree

Abstract

In the present paper, we investigate weakly periodic p-adic generalized Gibbs measures for p-adic Ising model with an external field on the Cayley tree of order two. For a normal subgroup of the group representation of the Cayley tree we prove that there exists at least one unbounded weakly periodic (in particular, nonperiodic) p-adic generalized Gibbs measures for this model. Moreover, we show that if p is any odd prime then a phase transition occurs, if p = 2 then a quasi phase transition occurs for p-adic Ising model with an external field.