ANOMALOUS INTERFACE ROUGHENING: THE ROLE OF A GRADIENT IN THE DENSITY OF PINNING SITES

We study the effect on interface roughening of a gradient del p in the density of pinning sites p. We identify a new correlation length, which is a function of del p : xi similar to (del p)(-gamma/alpha), where alpha = nu(perpendicular to)/nu(parallel to) is the roughness exponent, and gamma = nu(perpendicular to)/(1+nu(perpendicular to)) The exponents nu(perpendicular to) and nu(parallel to) characterize the transverse and longitudinal correlation lengths. To investigate the effect of del p on the scaling properties of the interface in (1 + 1) and (2 + 1) dimensions, we calculate the critical concentration, p(c), and the exponents gamma and alpha from which nu(perpendicular to) and nu(parallel to) can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.