Random-field instability of the ferromagnetic state

Abstract

We consider an Ising model with infinite-ranged interaction with statistically independent site fields with Gaussian distribution. The model is solved exactly and exhibits both an independent spin phase and a ferromagnetic phase, separated by a line of second-order phase transitions. We also establish that the replica technique yields exact results in the present model but not in the related random exchange system. © 1977 The American Physical Society.