Off-perturbative states in disordered systems

TL;DR

This paper develops a systematic method for off-perturbative calculations in disordered systems, revealing non-analytic free energy contributions due to localized excitations in specific phases.

Contribution

It introduces a new scheme for off-perturbative analysis and applies it to random temperature and field Ising models, uncovering essential singularities.

Findings

Non-analytic contributions in free energy away from critical points

Essential singularities caused by localized instanton-like excitations

Application to random temperature and random field Ising models

Abstract

The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the critical point, in the paramagnetic phase of the random temperature model, and in the ferromagnetic phase of the random field one, the free energy contains non-analytic contributions which have the form of essential singularities. It is demonstrated that these contributions appear due to localized in space instanton-like excitations.