J. Phys. I France
Volume 7, Number 10, October 1997
Page(s) 1191 - 1200
J. Phys. I France 7 (1997) 1191-1200
DOI: 10.1051/jp1:1997116

Interface Dynamics at the Depinning Transition

Juan M. López1 and Miguel A. Rodríguez2

1  Department of Mathematics, Imperial College 180 Queen's Gate, London SW7 2BZ, UK
2  Instituto de Física de Cantabria (CSIC-UC), avenida de Los Castros, 39005 Santander, Spain

(Received 29 April 1997, accepted 18 June 1997)

We study the local scaling properties of driven interfaces in disordered media modeled by the Edwards-Wilkinson equation with quenched noise. We find that, due to the super-rough character of the interface close to the depinning transition, the local width exhibits an anomalous temporal scaling. It does not saturate at a characteristic time $t_{\rm s}(l)\sim l^z$ as expected, but suffers an anomalous temporal crossover to a different time regime $t^{\beta_*}$, where $\beta_*\simeq 0.21$. This is associated with the existence of a local roughness exponent $\alpha_{\rm loc}\simeq 1$ that differs from the global one $\alpha \simeq 1.2$. The relevance of the typical size of pinned sites regions near the critical point investigated and the definition of the critical depinning is discussed.

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