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 W₂ and W₄ and the skewness W₃ in the Kim-Kosterlitz (KK) and body-centered solid-on-solid (BCSOS) models. Our results agree with the stationary state proposed by L\"assig. The roughness exponents Wₙ~L^αₙ obey power counting αₙ=nα, and the amplitude ratios of the moments are universal. They have the same values in both models: W₃/W₂1.5=-0.27(1) and W₄/W₂²=+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 α converges well to the Kim-Kosterlitz-L\"assig value α=2/5. The FSS corrections to scaling in the BCSOS model are strong. Naive extrapolations yield a smaller value α0.38(1), but are still consistent with α=2/5 if the leading irrelevant corrections to the FSS scaling exponent are of order yᵢᵣ-0.6(2).