Dynamical universality classes of simple growth and lattice gas models

Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation functions of the heights and the dimer lattice gas variables are determined with high precision. Parallel random-sequential (RS) and two-sub-lattice stochastic dynamics (SCA) have been compared. The latter causes a constant correlation in the long time limit, but after subtracting it one can find the same height functions as in case of RS. On the other hand the ordered update alters the dynamics of the lattice gas variables, by increasing (decreasing) the memory effects for nonlinear (linear) models with respect to random-sequential. Additionally, we support the KPZ ansatz and the Kallabis-Krug conjecture in $2+1$ dimensions and provide a precise growth exponent value $\beta=0.2414(2)$. We show the emergence of finite size corrections, which occur long before the steady state roughness is reached.