Supersymmetry Breaking in Disordered Systems and Relation to Functional Renormalization and Replica-Symmetry Breaking
Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
Abstract
In this article, we study an elastic manifold
in quenched disorder in the limit of zero temperature. Naively it is
equivalent to a free theory with elasticity in Fourier-space
proportional to k4 instead of k2, i.e. a model
without disorder in two space-dimensions less. This phenomenon, called
dimensional reduction, is most elegantly obtained using
supersymmetry. However, scaling arguments suggest, and functional
renormalization shows that dimensional reduction breaks down beyond
the Larkin length. Thus one equivalently expects a break-down of
supersymmetry. Using methods of functional renormalization, we show
how supersymmetry is broken. We also discuss the relation to
replica-symmetry breaking, and how our formulation can be put into
work to lift apparent ambiguities in standard functional
renormalization group calculations.
cond-mat/0411656 [pdf]
J. Phys. A 17 (2005) S1889-S1898 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.