Universality in two-dimensional Kardar-Parisi-Zhang growth

Abstract

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of the heights distribution are estimated. Results for the etching model, the ballistic deposition (BD) model and the temperature-dependent body-centered restricted solid-on-solid model (BCSOS) suggest the universality of the absolute value of the skewness S = W_3 / (W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of the skewness is the same of the parameter \lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015. For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value \alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.