One-step replica-symmetry-breaking solution of the Sherrington–Kirkpatrick model under aGaussian random field

Abstract

The Sherrington–Kirkpatrick model, in the presence of a Gaussian random field, is studiedthrough the replica formalism within a one-step replica-symmetry-breaking procedure. Thismodel treated in the replica-symmetry approximation does not exhibit a spin-glassphase, since the corresponding order parameter becomes trivially induced bythe random field. However, such a phase appears naturally through the presentapproach, being associated with the onset of replica-symmetry breaking. It isshown that the low-temperature negative-entropy problem, characteristic of thereplica-symmetry approximation, is practically resolved within this improved approach.Phase diagrams, the corresponding order parameters, and thermodynamic propertiesare computed; the present results are expected to be very close to the correctones, i.e., those that could be obtained from the full replica-symmetry-breakingprocedure.