2-loop functional renormalization group theory of the depinning transition
Pierre Le Doussal1, Kay Jörg Wiese2, Pascal Chauve3
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2Institute of Theoretical Physics, University of California at Santa Barbara, Santa Barbara, CA 93106-4030, USA
3CNRS-Laboratoire de Physique des Solides, Université de
Paris-Sud, Bât. 510, 91405 Orsay France
Abstract
We construct the field theory which describes the universal properties
of the quasi-static isotropic depinning transition for interfaces and
elastic periodic systems at zero temperature, taking properly into
account the non-analytic form of the dynamical action. This cures the
inability of the 1-loop flow-equations to distinguish between statics
and quasi-static depinning, and thus to account for the
irreversibility of the latter. We prove two-loop renormalizability,
obtain the 2-loop β-function and show the generation of
``irreversible'' anomalous terms, originating from the non-analytic
nature of the theory, which cause the statics and driven dynamics to
differ at 2-loop order. We obtain the roughness exponent ζ and
dynamical exponent z to order ε2. This
allows to test several previous conjectures made on the basis of the
1-loop result. First it demonstrates that random-field disorder does
indeed attract all disorder of shorter range. It also shows that the
conjecture ζ=ε/3 is incorrect, and allows to compute the
violations, as ζ=&epsilon/3 (1 + 0.14331ε),
ε=4-d. This solves a longstanding discrepancy with
simulations. For long-range elasticity it yields ζ=ε/3 (1
+ 0.39735 ε), &epsilon=2-d (vs. the standard prediction
ζ=1/3 for d=1), in reasonable agreement with the most
recent simulations. The high value of ζ approximately 0.5 found
in experiments both on the contact line depinning of liquid Helium and
on slow crack fronts is discussed.
cond-mat/0205108 [pdf]
Phys. Rev. B 66 (2002) 174201 [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.