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

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.

8 pages, 5 figures, final version with minor modifications to be published in Physical Review Letters

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• Canonical equilibrium of mean-field $O(n)$~models in the presence of random fields