VARIATIONAL STUDY OF THE RANDOM-FIELD XY MODEL

A disorder-dependent Gaussian variational approach is applied to the d -dimensional ferromagnetic XY model in a random field. The randomness yields a nonextensive contribution to the variational free energy, imp lying a random mass term in correlation functions. The Imry-Ma low-tem perature result, concerning the existence (d>4) or absence (d<4) of lo ng-range order is obtained in a transparent way. The physical picture which emerges below d=4 is that of a marginally stable mixture of doma ins. We also calculate within this variational scheme, disorder-depend ent correlation functions, as well as the probability distribution of the Imry-Ma domain size.