Application of p-adic analysis to models of breaking of replica symmetry

Methods of p-adic analysis are applied to the investigation of spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for th e Parisi replica matrix is given and, moreover, the Parisi replica matrix i n models of spontaneous breaking of the replica symmetry in the simplest ca se is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also, the model of hierarchical diffusion (that was propo sed to describe relaxation of spin glasses) is investigated using p-adic an alysis.