We solve a long-standing puzzle in statistical mechanics of disordered systems. By performing a high-statistics simulation of the $D=3$ 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 the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.

• Received 20 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.227201