Higher correlations, universal distributions and finite size scaling in the field theory of depinning
Pierre Le Doussal1, Kay Jörg Wiese2
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2KITP, University of California at Santa Barbara, Santa
Barbara, CA 93106-4030, USA
Abstract
Recently we constructed a renormalizable
field theory up to two loops for the quasi-static depinning of elastic
manifolds in a disordered environment. Here we explore further
properties of the theory. We show how higher correlation functions of
the displacement field can be computed. Drastic simplifications occur,
unveiling much simpler diagrammatic rules than anticipated. This is
applied to the universal scaled width-distribution. The expansion in
d=4-epsilon predicts that the scaled distribution coincides to the
lowest orders with the one for a Gaussian theory with propagator
G(q)=1/qd+2ζ, ζ being the roughness
exponent. The deviations from this Gaussian result are small and
involve higher correlation functions, which are computed here for
different boundary conditions. Other universal quantities are defined
and evaluated: We perform a general analysis of the stability of the
fixed point. We find that the correction-to-scaling exponent is
ω=-ε and not -ε/3 as used in the analysis of some
simulations. A more detailed study of the upper critical dimension is
given, where the roughness of interfaces grows as a power of a
logarithm instead of a pure power.
cond-mat/0301465 [pdf]
Phys. Rev. E 68 (2003)
046118 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.