Bifractality in one-dimensional Wolf-Villain model

TL;DR

This study uses multifractal analysis to investigate the scaling behavior of the one-dimensional Wolf-Villain model, revealing a bifractal signature and transient universality classes related to surface growth regimes.

Contribution

It introduces a multifractal detrended fluctuation analysis to characterize the complex scaling properties of the Wolf-Villain model, highlighting its bifractal nature and transient universality.

Findings

Long-wavelength fluctuations are consistent with the Edwards-Wilkinson class.

A bifractal signature indicates different regimes at short and long wavelengths.

The model exhibits MBE-like behavior at short wavelengths.

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 mounded surface morphologies for long time scales (up to $10^9$ monolayers) and its universality class remains controversial. Our results for the multifractal exponent $\tau(q)$ reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edward-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.