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Bifractality in the one-dimensional Wolf-Villain model
Edwin E Mozo Luis1, Silvio C Ferreira2,3, Thiago A de Assis1,4
1Instituto de Física, <a href="https://ror.org/02rjhbb08">Universidade Federal Fluminense</a>, Avenida Litorânea s/n, 24210-340, Niterói, RJ, Brazil.
Abstract:
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.
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