Dynamics of Gaussian interface models

Abstract

The relaxational dynamics of an initially flat ($d\ensuremath{-}1$)-dimensional interface in a $d$-dimensional system is modeled by the unweighted Gaussian model defined on a lattice and obeying Langevin dynamics. The interface width is calculated and is found to grow to its equilibrium value via three distinct limiting regimes, each containing different growth laws. Results are presented for $d=2 \mathrm{and} 3$ with scaling properties and limiting behavior in full agreement with previous continuum models and simulations of kinetic growth models.