Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking

TL;DR

This paper employs a nonperturbative functional renormalization group approach in superfield formalism to analyze supersymmetry and its spontaneous breaking in the random field Ising model, revealing critical dimensions and exponents.

Contribution

It introduces a supersymmetry-compatible nonperturbative approximation within the NP-FRG framework to study supersymmetry breaking in the RFIM.

Findings

Supersymmetry breaks spontaneously below d ≈ 5.1.

Broken supersymmetry leads to the failure of dimensional reduction.

Critical exponents match numerical estimates in d=3 and d=4.

Abstract

We apply the nonperturbative functional renormalization group (NP-FRG) in the superfield formalism that we have developed in the preceding paper to study long-standing issues concerning the critical behavior of the random field Ising model. Through the introduction of an appropriate regulator and a supersymmetry-compatible nonperturbative approximation, we are able to follow the supersymmetry, more specifically the superrotational invariance first unveiled by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)], and its spontaneous breaking along the RG flow. Breaking occurs below a critical dimension dDR \simeq 5.1, and the supersymmetry-broken fixed point that controls the critical behavior then leads to a breakdown of the "dimensional reduction" property. We solve the NP-FRG flow equations numerically and determine the critical exponents as a function of dimension down to d < 3, with a good agreement in d = 3 and d = 4 with the existing numerical estimates.