Eur. Phys. J. B 15, 149-153 (2000)
https://doi.org/10.1007/s100510051109

Dynamic exponent in extremal models of pinning

¹ Laboratoire de Physique et de Mécanique des Milieux Hétérogènes, École Supérieure de Physique et Chimie Industrielles de Paris, 10 rue Vauquelin, 75231 Paris Cedex 05, France
² Université de Lyon I, 43 boulevard du 11 Novembre 1918, 69622 Villeurbanne, France
³ Laboratoire Surface du Verre et Interfaces, Unité Mixte de Recherche CNRS/Saint-Gobain, 39 Quai Lucien Lefranc, BP 135, 93303 Aubervilliers Cedex, France

Received: 27 August 1999
Published online: 15 May 2000

Abstract

The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, , is the classical means to have access to the dynamic exponent. However, in the case of front propagation in quenched disorder via extremal dynamics, we show that the initial increase in front roughness implies an extra dependence over the system size which comes from the fact that the activity is essentially localized in a narrow region of space. We propose an analytic expression for the β exponent and confirm this for different models (crack front propagation, Edwards-Wilkinson model in a quenched noise etc.).