Edwards–Wilkinson depinning transition in fractional Brownian motion background

Abstract

AbstractThere are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards–Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time $$T^*$$ T ∗ that separates the dynamics into two distinct regimes: for $$T>T^*$$ T > T ∗ , we observe the typical behavior of pinned surfaces, while for $$T<T^*$$ T < T ∗ , the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ($$H<0.5$$ H < 0.5 ) and correlated ($$H>0.5$$ H > 0.5 ) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent $$\theta$$ θ to increase monotonically with H.