Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions

TL;DR

This study uses high-precision simulations to analyze the critical behavior of the four-dimensional random-field Ising model, revealing a single universality class and challenging existing theoretical predictions.

Contribution

It provides the first comprehensive set of critical exponents for the 4D RFIM, showing deviations from perturbative renormalization group predictions.

Findings

The 4D RFIM belongs to a single universality class.

Dimensional reduction does not hold in four dimensions.

Three independent critical exponents are necessary to describe the transition.

Abstract

By performing a high-statistics simulation of the $D=4$ random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions: (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to described the transition.