Abstract
In this paper, 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 inN dimensions, and give the exact solution forN →ɛ 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.
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