Lowering of Dimensionality in Phase Transitions with Random Fields

Abstract

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 ($d\ensuremath{-}2$)-dimensional pure system. Heuristic arguments are given to discuss both this result and the random-field Ising model for $2<d<6$.