Manifolds in random media: Beyond the variational approximation

TL;DR

This paper derives the first correction beyond the variational approximation for manifolds in random media, providing explicit formulas and analyzing their behavior in a high-temperature phase of a classical particle model.

Contribution

It presents a closed-form expression for 1/d corrections to the self-energy, advancing understanding beyond the variational approximation in disordered systems.

Findings

Corrections diverge at the transition temperature.

Explicit formulas for high-temperature phase corrections.

Comparison with previous analytical and numerical results.

Abstract

In this paper we give a closed form expression for the $1/d$ corrections to the self-energy characterizing the correction function of a manifold in random media. This amounts to the first correction beyond the variational approximation. At this time we were able to evaluate this corrections in the high temperature ``phase'' of the notorious toy-model describing a classical particle subject to the influence of both a harmonic potential and a random potential. Although in this phase the correct solution is replica symmetric the calculation is non-trivial. The outcome is compared with previous analytical and numerical results. The corrections diverge at the ``transition'' temperature.