When orthogonal detrending matters in roughness scaling.

Abstract

Determining the local roughness exponent α_{l} in nonequilibrium surface growth is challenging when transient morphologies with long crossover times, such as those in Villain-Lai-Das Sarma (VLDS) models, obscure the asymptotic regime. It was only recently that numerical simulations of VLDS lattice models revealed that Optimal Detrended Fluctuation Analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)2470-004510.1103/PhysRevE.95.042801] yields α_{l} values consistent with renormalization-group predictions for this class, even in transient regimes. However, a quantitative analytical framework explaining this agreement has been missing. Here, we close this gap by deriving how ODFA suppresses geometric corrections from local slope and curvature through the orthogonal projection of height fluctuations onto the local polynomial trend. We show that slope-induced corrections decay more slowly than curvature-induced ones, thereby dominating intermediate-scale biases. Our theoretical predictions are corroborated by numerical simulations of the Clarke-Vvedensky and Das Sarma-Tamborenea lattice models (with noise reduction), which confirm the predicted correction exponents in the small local-slope regime and the expected hierarchy in the suppression of slope and curvature effects.