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

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.

References in corpus (4)

• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
• Thin film growth models with long surface diffusion lengths
• Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

Cited by in corpus (4)

• The Kardar-Parisi-Zhang exponents for the $2+1$ dimensions
• Universal scaling relation for growth phenomena
• Modeling of nonequilibrium surface growth by a limited mobility model with distributed diffusion length
• Effects of a kinetic barrier on limited-mobility interface growth models