Marzio Cassandro, Enza Orlandi, Pierre Picco, and Maria Eulalia Vares
One-dimensional random field Kac's model:localization of the phases.
(961K, postscript)
ABSTRACT. We study the typical profiles of a one dimensional random field
Kac model, for values of the temperature and magnitude of the field
in the region of the two absolute minima for the free
energy of the corresponding random field Curie Weiss model.
We show that, for a set of realizations of the random field of
overwhelming probability, the localization of the two phases
corresponding to the previous minima is completely determined.
Namely, we are able to construct random intervals tagged with a
sign, where typically, with respect to the infinite volume Gibbs
measure, the profile is rigid and takes, according to the sign,
one of the two values corresponding to the previous minima.
Moreover, we characterize the transition from one phase to the other.