SURFACE ROUGHENING WITH QUENCHED DISORDER IN d-DIMENSIONS

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent alpha = 0.63 0.01 (d =1+1) and alpha = 0.48 +/- 0.02 (d = 2 + 1) are in good agreement with our recent experiments. We study also the diode-resistor percolation on a Cayley tree. We find that P-infinity similar to exp(-A/root p(c)-p), thus suggesting that the critical exponent for P-infinity similar to (p(c)-p)(beta p) , beta(p) = infinity and that the upper critical dimension in this problem is d = d(c) = infinity. Other critical exponents on the Cayley tree are: tau = 3, v(parallel to) = nu(perpendicular to) = gamma = sigma = 0. The exponents related to roughness are: alpha = beta = 0, z = 2.