Supersymmetric Spin Glass

TL;DR

This paper investigates a supersymmetric four-dimensional spin glass model, revealing a moduli space of infrared fixed points and identifying phases with and without replica symmetry, including a spin glass phase.

Contribution

It introduces a supersymmetric spin glass model and analyzes its phase structure and fixed points at the one-loop level, highlighting the presence of a spin glass phase.

Findings

Infrared fixed points form a moduli space RP^2.

Two phases identified: with and without replica symmetry.

Spin glass phase characterized by an unstable trivial fixed point.

Abstract

The evidently supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta-function form the moduli space $M = RP^2$ where two types of phases were found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase which may be interpreted as a spin glass phase.