Supersymmetry and its spontaneous breaking in the random field Ising model

TL;DR

This paper reformulates the functional renormalization group for the random field Ising model using superfield formalism, revealing supersymmetry breaking below a critical dimension and its impact on critical behavior and exponents.

Contribution

It introduces a superfield formalism to analyze supersymmetry and its spontaneous breaking in the RFIM within the FRG framework, clarifying longstanding puzzles.

Findings

Supersymmetry breaks below dimension ~5.1

Dimensional reduction fails below critical dimension

Critical exponents vary with dimension and involve three independent exponents

Abstract

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the FRG flow. Breaking is shown to occur below a critical dimension $d_{DR}\simeq 5.1$ and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.