Random-energy model in random fields

TL;DR

This paper analyzes the random-energy model under random fields, providing exact solutions in different ensembles and exploring phase diagrams, revealing unique phenomena like tricritical points and first-order transitions.

Contribution

It offers the first exact solutions of the random-energy model with random fields in both microcanonical and canonical ensembles, including detailed phase diagram analysis.

Findings

Bimodal fields can induce tricritical points and first-order transitions.

Phase diagrams show complex behavior with paramagnetic and mixed phases.

Exact solutions enhance understanding of disordered systems with random fields.

Abstract

The random-energy model is studied in the presence of random fields. The problem is solved exactly both in the microcanonical ensemble, without recourse to the replica method, and in the canonical ensemble using the replica formalism. The phase diagrams for bimodal and Gaussian random fields are investigated in detail. In contrast to the Gaussian case, the bimodal random field may lead to a tricritical point and a first-order transition. An interesting feature of the phase diagram is the possibility of a first-order transition from paramagnetic to mixed phase.