The Sherrington–Kirkpatrick model in the presence of a bimodal random field: a one-stepreplica-symmetry-breaking approach

Abstract

The infinite-range-interaction Ising spin glass in the presence of a bimodal random field isinvestigated through the replica method. A one-step replica-symmetry-breakingprocedure is considered, and its results are compared to previous ones, obtained in thereplica-symmetry approximation. An analysis of the thermodynamic properties at lowtemperatures shows that the one-step replica-symmetry-breaking produces a substantialamelioration with respect to the replica-symmetric solution; in particular, thelow-temperature negative-entropy problem is practically resolved within this improvedapproach. A curious aspect in replica-symmetric phase diagrams concerns the border of theferromagnetic phase, which for sufficiently high values of the field may present one or eventwo tricritical points. In this latter case, it is shown that the higher-temperature tricriticalpoint remains; however, the low-temperature one disappears within the one-stepreplica-symmetry-breaking procedure, yielding a first-order critical frontier down to zerotemperature.