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

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.

8 pages, 8 figures, 1 table ; supplemental material appended at the end ; version to be published in Phys. Rev. Lett