Wetting versus layering near the roughening transition in the three-dimensional Ising model

Ising models with free surfaces where a surface field H₁ competes with the bulk field H exhibit wetting phenomena at temperatures T above the roughening transition temperature TR, while for TTR layering transitions occur. In our previous Monte Carlo study of this model [Phys. Rev. B 37, 1745 (1988)] we posed the problem of how these two very different surface phase-transition phenomena can be integrated into a common phase diagram. Here we present new Monte Carlo results obtained on very large lattices, using an L×{}L×{}D thin-film geometry with L up to 512 and D up to 80, where the exchange Jₛ in the two free L×{}L surfaces is allowed to differ from the exchange J in the bulk. For Jₛ/J=0.5 we find that if H₁ is varied for H=0 and T{}TR the layering sequence starts with a transition in the third layer, the first two layers behaving smoothly with H₁. However, for Jₛ/J=1 the layering sequence starts with the second layer and only the first layer behaves smoothly. On the other hand, for Jₛ slightly exceeding J we find that the layering transitions of the first three layers coincide, and this transition develops into the first-order wetting transition for T{}TR. This latter behavior was not predicted by the previous phenomenological treatment. However, a complete clarification of the surface phase diagram of the Ising model would require extreme effort and cannot yet be provided by present simulation techniques.