Scale Invariant Dynamics of Surface Growth
Abstract
We describe in detail and extend a recently introduced nonperturbative renormalization group (RG) method for surface growth. The scale invariant dynamics which is the key ingredient of the calculation is obtained as the fixed point of a RG transformation relating the representation of the microscopic process at two different coarse-grained scales. We review the RG calculation for systems in the Kardar-Parisi-Zhang universality class and compute the roughness exponent for the strong coupling phase in dimensions from 1 to 9. Discussions of the approximations involved and possible improvements are also presented. Moreover, very strong evidence of the absence of a finite upper critical dimension for KPZ growth is presented. Finally, we apply the method to the linear Edwards-Wilkinson dynamics where we reproduce the known exact results, proving the ability of the method to capture qualitatively different behaviors.
Cite
@article{arxiv.cond-mat/9904434,
title = {Scale Invariant Dynamics of Surface Growth},
author = {C. Castellano and M. Marsili and M. A. Munoz and L. Pietronero},
journal= {arXiv preprint arXiv:cond-mat/9904434},
year = {2009}
}
Comments
18 pages, 15 figures, accepted for publication in Phys. Rev. E