SCALING PROPERTIES OF DRIVEN INTERFACES IN DISORDERED MEDIA

We perform a systematic study of several models that have been propose d for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes. (i) O ne of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson (QEW), can be described by a Langevin equat ion similar to the Edwards-Wilkinson equation, but with quenched disor der. We find that for the DPD universality class, the coefficient lamb da of the nonlinear term diverges at the depinning transition, while f or the QEW universality class, either lambda = 0 or lambda --> 0 as th e depinning transition is approached. The identification of the two un iversality classes allows us to better understand many of the results previously obtained experimentally and numerically. However, we find t hat some results cannot be understood in terms of the exponents obtain ed for the two universality classes at the depinning transition. In or der to understand these remaining disagreements, we investigate the sc aling properties of models in each of the two universality classes abo ve the depinning transition. For the DPD universality class, we find f or the roughness exponent alpha(P) = 0.63 +/- 0.03 for the pinned phas e and alpha(M) = 0.75 +/- 0.05 for the moving phase. For the growth ex ponent, we find beta(P) = 0.67 +/- 0.05 for the pinned phase and beta( M) = 0.74 +/- 0.06 for the moving phase. Furthermore, we find an anoma lous scaling of the prefactor of the width on the driving force. A new exponent (phi(M) = -0.12 +/- 0.06, characterizing the scaling of this prefactor, is shown to relate the values of the roughness exponents o n both sides of the depinning transition. For the QEW universality cla ss, we find that alpha(P) approximate to alpha(M) = 0.92 +/- 0.04 and beta(P) approximate to beta(M) = 0.86 +/- 0.03 are roughly the same fo r both the pinned and moving phases. Moreover, we again find a depende nce of the prefactor of the width on the driving force. For this unive rsality class, the exponent phi(M) = 0.44 +/- 0.05 is found to relate the different values of the local crp and global roughness exponent al pha(G) approximate to 1.23 +/- 0.04 at the depinning transition. These results provide us with a more consistent understanding of the scalin g properties of the two universality classes, both at and above the de pinning transition. We compare our results with all the relevant exper iments.