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.