Dynamics of driven interfaces in algebraically correlated random media

In this work we consider the dynamics of interfaces embedded in algebraical ly correlated two-dimensional random media. We study the isotropic percolat ion and the directed percolation lattice models away from and at their perc olation transitions. Away from the transition, the kinetic roughening of an interface in both of these models is consistent with the power-law correla ted Kardar-Parisi-Zhang universality class. Moreover, the scaling exponents are found to be in good agreement with existing renormalization-group calc ulations. At the transition, however, we find different behavior. In analog y to the case of a uniformly random background, the scaling exponents of th e interface can be related to those of the underlying percolation transitio n. For the directed percolation case, both the growth and roughness exponen ts depend on the strength of correlations, while for the isotropic case the roughness exponent is constant. For both cases, the growth exponent increa ses with the strength of correlations. Our simulations are in good agreemen t with theory. [S1063-651X(99)04003-9].