Derivation of the Functional Renormalization Group β-function at order 1/N for manifolds pinned by disorder
Pierre Le Doussal1, Kay Jörg Wiese1,2
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2Institut für Theoretische Physik, Universität Köln, Zülpicher Str. 77, 50937 Köln, Germany
Abstract
In an earlier publication, we have introduced a method to
obtain, at large N, the effective action for d-dimensional
manifolds in a N-dimensional disordered environment. This allowed to
obtain the Functional Renormalization Group (FRG) equation for
N=oo and was shown to reproduce, with no need for ultrametric
replica symmetry breaking, the predictions of the Mézard-Parisi
solution. Here we compute the corrections at order 1/N. We introduce
two novel complementary methods, a diagrammatic and an algebraic one,
to perform the complicated resummation of an infinite number of loops,
and derive the β-function of the theory to order 1/N. We
present both the effective action and the corresponding functional
renormalization group equations. The aim is to explain the conceptual
basis and give a detailed account of the novel aspects of such
calculations. The analysis of the FRG flow, comparison with other
studies, and applications, e.g. to the strong-coupling phase of the
Kardar-Parisi-Zhang equation are examined in a subsequent publication.
cond-mat/0406297 [pdf]
Nucl. Phys. B 701 (2004) 409-480 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.