Dynamical Renormalization Group Study of a Conserved Surface Growth with Anti-Diffusive and Nonlinear Currents

TL;DR

This paper uses one-loop dynamical renormalization group analysis to study a nonlinear conserved surface growth equation, revealing universality classes and stability properties, and contrasting analytical results with numerical simulations.

Contribution

It provides an analytical RG analysis of a nonlinear conserved surface growth model, identifying universality classes and stability differences for diffusive and anti-diffusive cases.

Findings

Growth with positive diffusion coefficient belongs to Edwards-Wilkinson universality class.

Anti-diffusive growth is unstable and does not match recent numerical simulations.

Analytical results highlight differences between diffusive and anti-diffusive surface growth behaviors.

Abstract

Based on dynamical renormalization group (RG) calculations to the one-loop order, the surface growth described by a nonlinear stochastic conserved growth equation, {\partial h \over \partial t} = \pm \nu_2 \nabla^2 h + \lambda\nabla \cdot (\nabla h)^3 + \eta, is studied analytically. The universality class of the growth described by the above equation with +{\nu_2} (diffusion) is shown to be the same as that described by the Edwards-Wilkinson (EW) equation (i.e. +\nu_2 and \lambda=0). In contrast our RG recursion relations manifest that the growth described by the above equation with {-\nu_2}(anti-diffusion) is an unstable growth and do not reproduce the recent results from a numerical simulation by J. M. Kim [Phys. Rev. E 52, 6267 (1995)].