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Scaling Exponents for Kinetic Roughening in Higher Dimensions | | T. Ala-Nissila
; T. Hjelt
; J. M. Kosterlitz
; O. Venäläinen
; | | Date: |
16 Dec 1992 | | Subject: | cond-mat | | 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 $ar G(t) sim t^{2eta}$ to estimate the scaling exponent $eta$. Using this method, we present a quantitative determination of $eta$ in d=3+1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determine $eta$ 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.} {f 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 $eta$. Within the accuracy of our data, we find no indication of an upper critical dimension up to d=7+1. | | Source: | arXiv, cond-mat/9212023 | | Services: | Forum | Review | PDF | Favorites | |
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