Why one needs a functional renormalization group to survive in a disordered world

TL;DR

This paper emphasizes the importance of functional renormalization group methods for analyzing strongly disordered systems, specifically elastic manifolds, highlighting non-analytic disorder distributions and advanced theoretical solutions.

Contribution

It introduces a renormalizable field theory for disordered elastic manifolds beyond 2-loop order and provides exact solutions in the large N limit, comparing different theoretical approaches.

Findings

Disorder distribution becomes non-analytic after renormalization.

Exact solution for elastic manifolds in infinite N limit.

Effective action at order 1/N reported.

Abstract

In these proceedings, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss how a renormalizable field theory can be constructed even beyond 2-loop order. We then consider an elastic manifold embedded in N dimensions, and give the exact solution for N to infinity. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. Finally, the effective action at order 1/N is reported.