Numerical study of roughness distributions in nonlinear models of interface growth

TL;DR

This study investigates the shapes of roughness distributions in nonlinear interface growth models, confirming expected scaling behaviors and revealing distinct tail behaviors in different models and dimensions.

Contribution

It provides the first detailed analysis of roughness distribution shapes in KPZ and VLDS class models across one and two dimensions.

Findings

KPZ models in 2D show stretched exponential tails with asymmetry.

VLDS models in 1D have Gaussian tails; in 2D, exponential tails.

Distributions differ from those of 1/f^α noise interfaces.

Abstract

We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi and Zhang (KPZ) and in the Villain, Lai and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm the expected scaling of the distribution and show a stretched exponential tail approximately as exp[-x^(0.8)], with a significant asymmetry near the maximum. Conserved restricted solid-on-solid models belonging to the VLDS class were simulated in d=1 and d=2. The tail in d=1 has the form exp(-x^2) and, in d=2, has a simple exponential decay, but is quantitatively different from the distribution of the linear fourth-order (Mullins-Herring) theory. It is not possible to fit any of the above distributions to those of 1/f^\alpha noise interfaces, in contrast with recently studied models with depinning transitions.