Simulated equilibrium and nonequilibrium interfaces in a lattice model

We have studied the properties of equilibrium and nonequilibrium (d-1)-dimensional interfaces via Monte Carlo simulations of a d-dimensional solid-on-solid model with d=2 and 3. At equilibrium, we examine the intrinsic width of the interface and the interfacial profile as functions of both the lateral size L of the system and the applied gravitational field g; we have studied also the height-height correlation function as a function of both separation and g in two dimensions. Our results are consistent with theories of these properties relying on exact (in an appropriate limit) solution of the model for the case of d=2 and on capillary-wave theory for d=3. The nonequilibrium interfaces studied are those which arise between a growing wetting film and a bulk phase. We look at the intrinsic width of the interface and at the interfacial profile in the large-L limit as functions of time and of the interaction between the substrate and adsorbate. For d-1 equal to both 1 and 2, and for all adsorbate-substrate potentials used, the width grows at a rate which is independent of this potential; the rate is consistent with fluctuation-dominated growth mechanisms. The profiles have the same shape as the equilibrium profiles. In particular we find for d-1=1 that the width varies with time as w∼$t^{1/4}$, which is the same as the rate of growth of the film thickness in the fluctuation regime.