Growth Models And The Question Of Universality Classes

Abstract

In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different universality classes, i.e. they are described by different differential equations. In the present paper we describe a mapping of ``growth rules'' to differential operators and give plausibility arguments for this mapping. We illustrate the validity of our theory by applying it to published results.

Cited by in corpus (4)

• Numerical study of discrete models in the class of the nonlinear molecular beam epitaxy equation
• Finite-size effects in roughness distribution scaling
• Maximal and minimal height distributions of fluctuating interfaces
• Multifractal scaling of flux penetration in the Iron-based Superconductor Ba(Fe${}_{0.93}$Co${}_{0.07}$)${}_2$As${}_2$