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 the Parisi replica matrix is given and, moreover, the Parisi replica matrix in models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also, the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) is investigated using p-adic analysis.