Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems

TL;DR

This paper explores the connection between spontaneous and explicit replica symmetry breaking in disordered systems, establishing their equivalence and enabling new analytical approaches to spin-glass phenomena.

Contribution

It proves the equivalence between the replicon operator and the operator signaling symmetry breakdown with explicit sources, facilitating advanced analysis of disordered systems.

Findings

Proves the equivalence between spontaneous and explicit replica symmetry breaking.

Establishes a foundation for using functional renormalization group in disordered systems.

Enables new insights into spin-glass behavior in finite dimensions.

Abstract

We investigate the relation between spontaneous and explicit replica symmetry breaking in the theory of disordered systems. On general ground, we prove the equivalence between the replicon operator associated with the stability of the replica symmetric solution in the standard replica scheme and the operator signaling a breakdown of the solution with analytic field dependence in a scheme in which replica symmetry is explicitly broken by applied sources. This opens the possibility to study, via the recently developed functional renormalization group, unresolved questions related to spontaneous replica symmetry breaking and spin-glass behavior in finite-dimensional disordered systems.