SCALING EXPONENTS FOR KINETIC ROUGHENING IN HIGHER DIMENSIONS

We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d = 7 + 1. To this end, we study the restricted solid-on-solid growth model, for which we employ a novel fitting ansatz for the spatially averaged height correlation function GBAR(t) approximately t2beta to estimate the scaling exponent beta. Using this method, we present a quantitative determination of beta in d = 3 + 1 and 4 + 1 dimensions. To check the consistency of these results, we also compute the interface width and determine beta and chi from it independently. Our results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates for beta. Within the accuracy of our data, we find no indication of an upper critical dimension up to d = 7 + 1.