Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions

Abstract: The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth rule, and compare the estimated values with the previous numerical and experimental results. For the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these { discrete models with quenched disorder}. For full comparisons in the physically relevant spatial dimensions, we also perform numerically two distinct universality classes, including the quenched Edwards-Wilkinson (QEW), and the quenched Kardar-Parisi-Zhang (QKPZ) equations with and without external driving forces. The critical exponents of these {systems in the presence of quenched disorder} are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these {discrete systems with quenched disorder} in the (2+1)-dimensional cases, we present surface morphologies with various external driving forces during the saturated time regimes. The relationships between surface morphologies, scaling exponents and correlation length are also revealed.