Microstructure and velocity of field-driven solid-on-solid interfaces: Analytic approximations and numerical results

The local structure of a solid-on-solid interface in a two-dimensional kinetic Ising ferromagnet or attractive lattice-gas model with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field or chemical potential, is studied by an analytic mean-field, nonlinear-response theory [P. A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)], and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.