Scaling Exponents for Kinetic Roughening in Higher Dimensions

TL;DR

This paper presents extensive numerical simulations to estimate kinetic roughening scaling exponents in higher dimensions, revealing discrepancies with existing theories and suggesting no upper critical dimension up to 7+1.

Contribution

It introduces a novel fitting ansatz for the height correlation function and provides the first quantitative estimates of the exponent eta in dimensions 3+1 and 4+1.

Findings

Quantitative eta estimates in 3+1 and 4+1 dimensions.

Disagreement with existing theories and conjectures.

No evidence of an upper critical dimension up to 7+1.

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 $\bar G(t) \sim t^{2\beta}$ 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 [{\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 $\beta$. Within the accuracy of our data, we find no indication of an upper critical dimension up to d=7+1.