Kuelske C.
Stability for a continuous SOS-interface model
in a randomly perturbed periodic potential
(284K, PS)
ABSTRACT. We consider the Gibbs-measures of continuous-valued height
configurations on the $d$-dimensional integer lattice in
the presence a weakly disordered potential. The potential is
composed of Gaussians having random location and random
depth; it becomes periodic under shift of the interface
perpendicular to the base-plane for zero disorder.
We prove that there exist localized interfaces with probability
one in dimensions $d\geq 3+1$, in a `low-temperature' regime.
The proof extends the method of continuous-to-discrete single-
site coarse graining that was previously applied by the author
for a double-well potential to the case of a non-compact image
space. This allows to utilize parts of the renormalization
group analysis developed for the treatment of a contour
representation of a related integer-valued SOS-model in [BoK1].
We show that, for a.e. fixed realization of the disorder, the
infinite volume Gibbs measures then have a representation as
superpositions of massive Gaussian fields with centerings that
are distributed according to the infinite volume Gibbs measures
of the disordered integer-valued SOS-model with exponentially
decaying interactions.