The growth and possible wetting behaviors of an adsorbed film are studied employing a solid-on-solid model in the presence of a hard wall and external potential $V\left(h\right)\mathrm{}$ which is of long range. The model is analyzed with the use of position-space renormalization-group methods within the Migdal approximation. The existence of wetting transitions and their nature depends on the asymptotic behavior of $V\left(h\right)\mathrm{}$ at large distances. We find that critical wetting cannot take place in this model. From what is known of $V\left(h\right)\mathrm{}$, we conclude that wetting can be observed only along the gas-liquid phase boundary; however, first-order transitions between thin and thick films, which may be experimentally difficult to distinguish from wetting, can be observed along any phase boundary. The nature of the global phase diagram depends on the form of $V\left(h\right)\mathrm{}$ and several general behaviors are presented. In particular, in the layering subregime we find that the limit of layering critical points is indeed the bulk roughening temperature as had been suggested by de Oliveira and Griffiths. The scaling of these layering critical points is given explicitly.

• Received 13 February 1984

DOI:https://doi.org/10.1103/PhysRevB.30.3830