Monte Carlo studies of wetting, interface localization and capillary condensation

We present a brief review of Monte Carlo simulations of ferromagnetic Ising lattices in a film geometry with surface magnetic fields. The seminal work of Nakanishi and Fisher [Phys. Rev. Lett. 49:1565 (1982)] showed how phase transitions in such models are related to wetting in systems with short range forces; and we will show how theoretical concepts about critical and tricritical wetting, interface localization-delocalization, and capillary condensation can be tested in this and similar models. After reviewing the qualitative, phenomenological description of these phenomena on a mean field level, we will summarize predictions of scaling theories. Comments will be made about the models studied and simulation techniques as well as the specific problems that occur in the relevant finite size scaling analysis. The resulting simulational data have prompted considerable new theoretical efforts, but there are still unsolved problems with respect to critical wetting. We will also present results for interface localization-delocalization transitions in both Ising models and lattice polymer mixtures in a thin film geometry and show that theory can account for many, but not all, aspects of the simulations. In systems with asymmetric boundary fields rather complex phase diagrams can result, and these should be relevant for corresponding experiments. The simulational evidence is fully compatible with the scaling predictions of Fisher and Nakanishi [J. Chem. Phys. 75:5875 (1981)] on capillary condensation. To conclude we shall summarize the major unanswered theoretical questions in this rich field of inquiry.