The Functional Renormalization Group Treatment of Disordered
Systems: a Review
Kay Jörg Wiese
Institute of Theoretical Physics, University of California at
Santa Barbara, Santa Barbara, CA 93106-4030, USA
Abstract
We review current progress in the functional
renormalization group treatment of disordered systems. After an
elementary introduction into the phenomenology, we show why in the
context of disordered systems a functional renormalization group
treatment is necessary, contrary to pure systems, where
renormalization of a single coupling constant is sufficient. This
leads to a disorder distribution, which after a finite renomalization
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 1-loop order. We then discuss
an elastic manifold imbedded in N dimensions, and give the exact
solution for N -> oo. This is compared to predictions of the Gaussian
replica variational ansatz, using replica symmetry breaking. We
finally discuss depinning, both isotropic and anisotropic, and the
scaling function for the width distribution of an interface.
Proceedings for TH-2002 [pdf]
Ann. Henri Poincaré 4
(2003) 473-496 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.