Non-perturbative phenomena in the three-dimensional random field Ising model

TL;DR

This paper develops a systematic method to calculate non-perturbative contributions to the free energy in the 3D random field Ising model, revealing instanton-like excitations and their impact on phase transition behavior.

Contribution

It introduces a novel approach to evaluate non-perturbative effects in the 3D RFIM using instanton solutions and reduces complex equations to a simpler form related to the pure system.

Findings

Non-perturbative contributions arise from localized instanton-like excitations.

In D=3, the non-analytic contribution is explicitly calculated.

The phase transition nature in the 3D RFIM is discussed.

Abstract

The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space instanton-like excitations. It is shown that away from the critical region such instanton solutions are described by the set of the mean-field saddle-point equations for the replica vector order parameter, and these equations can be formally reduced to the only saddle-point equation of the pure system in dimensions (D-2). In the marginal case, D=3, the corresponding non-analytic contribution is computed explicitly. Nature of the phase transition in the three-dimensional random field Ising model is discussed.