# Evidence for Supersymmetry in the Random-Field Ising Model at D = 5

## TL;DR

This paper provides numerical evidence supporting supersymmetry in the five-dimensional random-field Ising model, confirming theoretical predictions at D=5 but not at D=4, through extensive finite-size scaling simulations.

## Contribution

The study offers the first high-precision numerical test of supersymmetry in the 5D random-field Ising model, validating theoretical relations at this dimension.

## Key findings

- Supersymmetry relations hold at D=5 with high accuracy.
- Supersymmetry predictions fail at D=4.
- Finite-size scaling method effectively tests supersymmetry.

## Abstract

We provide a non-trivial test of supersymmetry in the random-field Ising model at five spatial dimensions, by means of extensive zero-temperature numerical simulations. Indeed, supersymmetry relates correlation functions in a D-dimensional disordered system with some other correlation functions in a D-2 clean system. We first show how to check these relationships in a finite-size scaling calculation, and then perform a high-accuracy test. While the supersymmetric predictions are satisfied even to our high-accuracy at D=5, they fail to describe our results at D=4.