Stationary-state skewness in two-dimensional Kardar-Parisi-Zhang type growth

We present numerical Monte Carlo results for the stationary-state properties of KPZ-type growth in two-dimensional surfaces, by evaluating the finite size scaling (FSS) behavior of the second and fourth moments W-2 and W-4 and the skewness W-3 in the Kim-Kosterlitz (KK) and body-centered solid-on-solid (BCSOS) models. Our results agree with the stationary state proposed by Lassig. The roughness exponents W(n)similar to L-alpha n obey power counting alpha(n)=n alpha, and the amplitude ratios of the moments are universal. They have the same values in both models: W-3/W-2(1.5) = - 0.27(1) and W-4/W-2(2) = + 3.15(2). Unlike in one dimension, the stationary-state skewness is not tunable, but a universal property of the stationary-state distribution. The FSS corrections to scaling in the KK model are weak and a converges well to the Kim-Kosterlitz-Lassig value alpha = 2/5. The FSS corrections to scaling in the BCSOS model are strong. Naive extrapolations yield a smaller value alpha similar or equal to 0.38(1), but are still consistent with alpha = 2/5 if the leading irrelevant corrections to the FSS scaling exponent are of order y(ir) similar or equal to - 0.6(2). [S1063-651X(99)00503-6].