Lowering of dimensionality in phase transitions with random fields

We prove that to all orders in perturbation expansion, the critical exponents of a phase transition in a d-dimensional (4<d<6) system with short-range exchange and a random quenched field are the same as those of a (d-2)-dimensional pure system. Heuristic arguments are given to discuss both this result and the random-field Ising model for 2<d<6.