A REMARK ON THE LOW-TEMPERATURE BEHAVIOR OF THE SOS INTERFACE IN HALF-SPACE

We investigate the low-temperature phase diagram of the d-dimensional (d greater than or equal to 2) solid-on-solid (SOS) interface constrai ned to lie above a rigid wall to which it is attracted by a constant f orce. We prove uniqueness of the Gibbs state and exponentially fast co nvergence (in the diameter of the domain) of the finite-volume expecta tion of local observables, for all values of parameters where uniquene ss in the class of translation-periodic limit Gibbs states was establi shed previously. These domains of uniqueness are bordered by lines on which the system undergoes a layering transition.