Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance

TL;DR

This paper advances the nonperturbative functional renormalization group approach for the random field Ising model by employing a superfield formalism, incorporating ground-state dominance, and multiple system copies to analyze critical behavior and rare events.

Contribution

It introduces a superfield formalism for the nonperturbative RG of the RFIM, including ground-state dominance and multiple copies to capture full disorder cumulants and rare events.

Findings

Derived exact RG equations for disorder cumulants.

Extended supersymmetric description of critical behavior.

Accounted for ground-state dominance and rare events.

Abstract

We reformulate the nonperturbative functional renormalization group for the random field Ising model in a superfield formalism, extending the supersymmetric description of the critical behavior of the system first proposed by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)]. We show that the two crucial ingredients for this extension are the introduction of a weighting factor, which accounts for ground-state dominance when multiple metastable states are present, and of multiple copies of the original system, which allows one to access the full functional dependence of the cumulants of the renormalized disorder and to describe rare events. We then derive exact renormalization group equations for the flow of the renormalized cumulants associated with the effective average action.