Phase transitions in disordered systems: the example of the random-field   Ising model in four dimensions
  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. 
Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, and Nicolas   Sourlas
cond-mat.dis-nn