Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger

We consider a free lattice field (a harmonic crystal) with a hard wall cond ition and a weak pinning to the wall. We prove that in a weak sense the pin ning always dominates the entropic repulsion of the hard wall condition whe n the dimension is a least three. This contrasts with the situation in dime nsion one, where there is a so-called wetting transition, as has been obser ved by Michael Fisher. The existence of a wetting transition in the delicat e two-dimensional case was recently proved by Caputo and Velenik. (C) 2000 American Institute of Physics. [S0022-2488(00)00503-X].