Numerical study of roughness distributions in nonlinear models of interface growth

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(−x²) 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^α noise interfaces, in contrast with recently studied models with depinning transitions.