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

TL;DR

This paper applies p-adic analysis techniques to spin glass models, providing new mathematical expressions for replica matrices and exploring hierarchical diffusion phenomena related to symmetry breaking.

Contribution

It introduces p-adic expressions for the replica matrix and connects the Vladimirov operator to models of spontaneous replica symmetry breaking.

Findings

Derived a p-adic expression for the replica matrix

Expressed the replica matrix using the Vladimirov operator

Analyzed hierarchical diffusion in spin glasses using p-adic methods

Abstract

Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the 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) investigated using p-adic analysis.