Monte Carlo simulation of the growth of wetting layers

We present the first Monte Carlo study of the dynamics of the formation of the wet phase far from the wetting transition for a short-range attractive wall potential. A nearest-neighbor, simple-cubic, ferromagnetic Ising lattice gas with single spin-flip dynamics in a slab geometry (L×L cross section) is used. We show that there are two distinct dynamical regimes with crossover from fluctuation-dominated logarithmic growth for large L and short time t to quasi-one-dimensional diffusive growth for small L and large t. For any finite system, the long-time behavior (i.e., t≫$L^4$[ln(L${)}^2$]) is predicted to always be quasi-one-dimensionally diffusive in nature.