Scaling Exponents for Kinetic Roughening in Higher Dimensions

Abstract

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 {\it ansatz} for the spatially averaged height correlation function $\bar G(t) \sim t^{2β}$ to estimate the scaling exponent $β$. Using this method, we present a quantitative determination of $β$ in d=3+1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determine $β$ and $χ$ 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 [{\it Phys. Rev. Lett.} {\bf 64}:1405 (1990)] for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates for $β$. Within the accuracy of our data, we find no indication of an upper critical dimension up to d=7+1.