  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.
