WETTING VERSUS LAYERING NEAR THE ROUGHENING TRANSITION IN THE 3-DIMENSIONAL ISING-MODEL

Ising models with free surfaces where a surface field H-1 competes with the bulk field H exhibit wetting phenomena at temperatures T above the roughening transition temperature T(R), while for T < T(R) 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 X L X D thin-film geometry with L up to 512 and D up to 80, where the exchange J(s) in the two free L X L surfaces is allowed to differ from the exchange J in the bulk. For J(s)/J = 0.5 we find that if H-1 is varied for H = 0 and T less than or similar T(R) the layering sequence starts with a transition in the third layer, the first two layers behaving smoothly with H-1. However, for J(s)/J = 1 the layering sequence starts with the second layer and only the first layer behaves smoothly. On the other hand, for J(s) 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 less than or similar T(R). 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.