Dynamical renormalization group analysis of fourth-order conserved growth nonlinearities.

Abstract

A nonlinear stochastic fourth-order conserved growth equation \ensuremath{\partial}h/\ensuremath{\partial}t=-${\ensuremath{\nu}}_{4}$${\mathrm{\ensuremath{\nabla}}}^{4}$h + ${\ensuremath{\lambda}}_{22}$${\mathrm{\ensuremath{\nabla}}}^{2}$(\ensuremath{\nabla}h${)}^{2}$ +${\ensuremath{\lambda}}_{13}$\ensuremath{\nabla}(\ensuremath{\nabla}h${)}^{3}$+\ensuremath{\eta} has been studied analytically, using the perturbative dynamical renormalization group approach. One-loop calculation generates long-wavelength scaling properties of the known Edwards-Wilkinson universality class which has the corresponding equation \ensuremath{\partial}h/\ensuremath{\partial}t=${\ensuremath{\nu}}_{2}$${\mathrm{\ensuremath{\nabla}}}^{2}$h+\ensuremath{\eta}. Our result agrees with the recent numerical result of Kim and Das Sarma (unpublished) based on direct numerical integration. A two-loop calculation validates our conclusion, and we argue that our result holds to all orders in perturbative expansion.