# Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension

## TL;DR

This study accurately measures local roughness exponents for one-dimensional interface growth models in the nMBE universality class, confirming theoretical predictions and clarifying the nature of scaling corrections.

## Contribution

It introduces an optimized fluctuation analysis method that improves exponent estimation for models with strong scaling corrections in the nMBE class.

## Key findings

- ODFA outperforms standard methods in exponent estimation
- Exponents are in the range [0.96, 0.98], aligning with RG predictions
- Results support the absence of anomalous scaling in the nMBE class

## Abstract

We report local roughness exponents, $\alpha_{\text{loc}}$, for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval $\alpha_{\text{loc}}\in[0.96,0.98]$ consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form $\alpha_{\text{loc}}=1-\epsilon$ of the one-loop renormalization group analysis of the VLDS equation.