Functional Renormalization for Disordered Systems: Basic Recipes and Gourmet Dishes
Kay Jörg Wiese, Pierre Le Doussal
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France, and
KITP, University of California at Santa Barbara, Santa Barbara, CA 93106-4030, USA.
Abstract
We give a pedagogical introduction into the functional renormalization
group treatment of disordered systems. After a review of its
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 renormalization becomes non-analytic, thus overcoming the
predictions of the seemingly exact dimensional reduction. We discuss,
how the non-analyticity can be measured in a simulation or
experiment. We then construct a renormalizable field theory beyond
leading order. We discuss 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. We further consider random field
magnets, and supersymmetry. We finally discuss depinning, both
isotropic and anisotropic, and universal scaling function.
cond-mat/0611346 [pdf]
Markov Processes Relat. Fields 13 (2007) 777-818 [pdf]
[MR report]
Copyright (C) by Kay Wiese. Last edited June 9, 2020.