Surface melting and the surface phase diagram

We solve a spin-1 model at zero temperature which exhibits the analogue of surface melting as its triple point is approached, and study the effect of this phenomenon on the surface phase diagram of the system enclosed by walls. We note that when a thick film of the ‘‘solid’’ phase can adsorb on the walls, it is reasonable that it will do so all the way to the triple point. In this case, the surface phase diagram exhibits two distinct series of layering transitions in the region of the bulk ‘‘gas’’ phase. One of these is the well-known series by which the solid grows; the other is seen to be intimately related to the layering transitions associated with surface melting and is, therefore, the direct effect of such melting on the surface diagram. A single series of layering transitions appears in the region of the bulk ‘‘liquid’’ phase, and none in the solid. Effects of finite temperature and roughening are discussed and a schematic phase diagram proposed for the finite-temperature system, one which may be applicable to ${\mathrm{CF}}_4$ and ${\mathrm{C}}_2$ ${\mathrm{H}}_4$ adsorbed on graphite. When a thick film of the solid cannot adsorb on the walls, surface melting does not affect the surface phase diagram off of coexistence.