MAPPNG OF CRYSTAL-SURFACES ONTO THE 2-VERTEX MODEL

Within the solid-on-solid framework we map certain surfaces of a simpl e cubic crystal onto a five-vertex model. The mapping scheme used diff ers from the more common body-centered solid-on-solid mapping, which u ses a six-vertex model and is only suitable for interfaces whose latti ce splits naturally into two sublattices. In the five-vertex model the re is no touching of step lines and the arrow-reversal symmetry is bro ken by construction. After reviewing the exact solution of the five-ve rtex model and studying its phase diagram in the presence of an extern al field, we establish an isomorphism between some phases of the verte x model with the (100), (110) and (101BAR) faces of the simple cubic c rystal. We determine exactly the mean square height difference. If no field is applied the flat surfaces undergo a transition at a critical temperature, where the inclination of the surfaces begins to change, a nd roughening sets in. If, however, the inclination is kept constant b y applying a suitable field, the low-index flat (or high-index vicinal ) surfaces remain smooth (or rough) from zero up to infinite temperatu re, without undergoing any roughening transition.