Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

Alberto Rosso¹, Pierre Le Doussal², Kay Jörg Wiese²
¹ LPTMS; CNRS and Université Paris-Sud, UMR 8626, ORSAY CEDEX 91405, France.
²CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France, and
KITP, University of California at Santa Barbara, Santa Barbara, CA 93106-4030, USA.

Abstract

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Δ(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.

cond-mat/0610821 [pdf]
Phys. Rev. B 75 (2007) 220201 [pdf]