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 ($4<d<\mathrm{}6\mathrm{}$) system with short-range exchange and a random quenched field are the same as those of a ($d-2\mathrm{}$)-dimensional pure system. Heuristic arguments are given to discuss both this result and the random-field Ising model for $2<d<\mathrm{}6\mathrm{}$.