**Disorder relevance for pinning of random surfaces **

Hubert
Lacoin (IMPA)

(joint work with G. Giacomin)

Disorder
relevance is an important question in Statistical Mechanics. It can
be formulated as follows: "If the Hamiltonian of model is
modified by adding a small random perturbation, does it conserve a
phase transition with the same characteristics as that of the pure
model." A mathematical investigation of this matter is of course
possible only for models for which the phase transition is rigorously
understood in the pure setup, and our work concerns a very simple and
tractable model of surfaces in interaction with a defect plane.

The
surfaces is modeled by the graph of a Gaussian-Free-Field $\mathbb
Z^d$, $d\ge 2$, and the interaction is given by an energy reward for
each point of the graph whose height is in the interval $[-1,1]$. The
system undergoes a wetting transition from a localized phase to a
delocalized one, when the mean energy of interaction varies.

We
investigate the modification of the free-energy curve induced by the
introduction of inhomogeneity in the interaction. We show that in a
certain sense the critical point is left invariant by the presence of
homogeneity, but that the localization transition becomes much
smoother.