Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

Abstract

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar–Parisi–Zhang (KPZ) universality class, in d = 1 + 1, for both flat and curved geometries. We analyzed two classes of models. In the isotropic models the non-universal parameters are uniform along the surface, whereas in anisotropic growth they vary. In the latter case, which produces curved surfaces, the statistics must be computed independently along fixed directions. The ansatz h = v∞t + (Γt)1/3χ + η, where χ is a Tracy–Widom (geometry-dependent) distribution and η is a time-independent correction, is probed. Our numerical analysis shows that the non-universal parameter Γ determined through the first cumulant leads to a very good accordance with the extended KPZ ansatz for all investigated models in contrast with the estimates of Γ obtained from higher order cumulants that indicate a violation of the generalized ansatz for some of the studied models. We associate the discrepancies to corrections of an unknown nature, which hampers an accurate estimation of Γ at finite times. The discrepancies in Γ via different approaches are relatively small but sufficient to modify the scaling law t−1/3 that characterizes the finite-time corrections due to η. Among the investigated models, we have revisited an off-lattice Eden model that supposedly disobeyed the shift in the mean scaling as t−1/3 and showed that there is a crossover to the expected regime. We have found model-dependent (non-universal) corrections for cumulants of order n ≥ 2. All investigated models are consistent with a further term of order t−1/3 in the KPZ ansatz.