Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth
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 the anisotropic growth they vary. In the latter case, that produces curved surfaces, the statistics must be computed independently along fixed directions. The ansatz $h=v_∞ t + (Γ t)^1/3χ+η$, where $χ$ is a Tracy-Widom (geometry-dependent) distribution and $η$ is a time-independent correction, is probed. We have verified that the non-universal parameter $Γ$ is determined more efficiently using the quantity $g_1=3t^2/3(\lrangleh_t-v_∞)\rightarrowΓ^1/3\lrangleχ$ than using the scaled second cumulant $g_2=\lrangleh^2_c/t^2/3$, which can be ruled by strong and/or puzzling corrections. The discrepancies in $Γ$ via different approaches are relatively small but sufficient to modify the scaling law $t^-1/3$ that characterize the finite-time corrections due to $η$. In particular, 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.