Asymptotic dynamic scaling behavior of the (1+1)-dimensional Wolf-Villain model

Bifractality in the one-dimensional Wolf-Villain model

We introduce a multifractal optimal detrended fluctuation analysis to study the scaling properties of the one-dimensional Wolf-Villain (WV) model for surface growth. This model produces coarsened surface morphologies for long timescales (up to 10^{9} monolayers) and its universality class remains an open problem. Our results for the multifractal exponent τ(q) reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edwards-Wilkinson (EW) universality class for negative and positive q values, respectively. Therefore, although the results corroborate that long-wavelength fluctuations belong to the EW class in the hydrodynamic limit, as conjectured in the recent literature, a bifractal signature of the WV model with an MBE regime at short wavelengths was observed.

Effects of a kinetic barrier on limited-mobility interface growth models

The role played by a kinetic barrier originated by out-of-plane step edge diffusion, introduced by Leal et al. [J. Phys.: Condens. Matter 23, 292201 (2011)JCOMEL0953-898410.1088/0953-8984/23/29/292201], is investigated in the Wolf-Villain and Das Sarma-Tamborenea models with short-range diffusion. Using large-scale simulations, we observe that this barrier is sufficient to produce growth instability, forming quasiregular mounds in one and two dimensions. The characteristic surface length saturates quickly indicating a uncorrelated growth of the three-dimensional structures, which is also confirmed by a growth exponent β=1/2. The out-of-plane particle current shows a large reduction of the downward flux in the presence of the kinetic barrier enhancing, consequently, the net upward diffusion and the formation of three-dimensional self-assembled structures.

Normal dynamic scaling in the class of the nonlinear molecular-beam-epitaxy equation

The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions d=1 and 2. In d=1, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to 0.1. Other VLDS models in d=1, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to 10(6) monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In d=2, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in d=1 and 2, in agreement with the theoretical predictions of Phys. Rev. Lett. 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.