On the repulsion of an interfaceabove a correlated substrate

We analyze a model of an interface fluctuating above arough substrate. It is based on harmonic crystals, or latticefree fields, indexed by ^d ,d 3. The phenomenon forwhich we want to get precise quantitative estimates is therepulsion effect of the substrate on the interface: thesubstrate is itself a random field, but its randomness isquenched (this generalizesthe widely considered case of a flat deterministic substrate).With respect to [2] in which the substrate has been taken to bean IID field, here the substrate is an harmonic crystal, as theinterface, and as such it is strongly correlated. We obtain theleading asymptotic behavior of the model in the limit of a veryextended substrate: we show in particular that, to leadingorder, the effect of an IID substrate cannot be distinguishedfrom the effect of an harmonic crystal substrate. We observehowever that, unlike in the IID substrate case, annealed andquenched models display sharply different features.