J. Phys. II France
Volume 2, Numéro 8, August 1992
Page(s) 1483 - 1488
DOI: 10.1051/jp2:1992214
J. Phys. II France 2 (1992) 1483-1488

Dynamics of interface depinning in a disordered medium

Thomas Nattermann1, Semjon Stepanow1, Lei-Han Tang1 and Heiko Leschhorn2

1  Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, D-5000 Köln 41, Germany
2  Theoretische Physik III, Ruhr-Universität Bochum, Postfach 102148, D-4630 Bochum, Germany

(Received 16 June 1992, accepted 22 June 1992)

The dynamics of a driven interface in a disordered medium close to the depinning threshold is analyzed. By a functional renormalization group scheme exponents characterizing the depinning transition are obtained to the first order in $\epsilon = 4-D>0$, where D is the interface dimension. At the transition, the dynamics is superdiffusive with a dynamical exponent $z=2-2\epsilon /9+O(\epsilon^{2})$, and the interface height difference over a distance L grows as $L^\zeta$ with $\zeta = \epsilon /3+O(\epsilon^{2})$. The interface velocity in the moving phase vanishes as $(F-F_{\rm c})^ \theta$ with $\theta =1-\epsilon /9+O(\epsilon^{2})$ when the driving force F approaches its threshold value $F_{\rm c}$.

64.60A - 47.55M - 75.10N - 75.60

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