Functional renormalization group at large N for random manifolds
Pierre Le Doussal1, Kay Jörg Wiese2
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2Institute for Theoretical Physics, University of California at Santa Barbara, CA 93106, USA
Abstract
We introduce a method, based on an exact calculation of the effective action
at large N, to bridge the gap between mean
field theory and renormalization in
complex systems. We apply it to a d-dimensional manifold
in a random potential
for large embedding space dimension N.
This yields a functional renormalization
group equation valid for any d, which contains both
the O(ε = 4-d) results
of Balents-Fisher and some of the non-trivial results of the Mezard-Parisi
solution thus shedding light on both. Corrections are computed at order O(1/N).
Applications to the problems of KPZ, random field and mode coupling in glasses
are mentioned.
cond-mat/0109204 [pdf]
Phys. Rev. Lett. 89 (2002) 125702 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.