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

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.