One-dimensional Random Field Kac's Model: Localization of the Phases
Marzio Cassandro, Dipartimento di Fisica, universita di Roma La Sapienza, Italy
Enza Orlandi, Dipartimento di Matematica, Universita di Roma Tre, Italy
Pierre Picco, CPT-CNRS, UMR 6207,Luminy Marseille, France
Maria Eulalia Vares, CBPF, Rio de Janeiro, Brasil
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 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.
The analysis extends the one done by Cassandro, Orlandi and Picco in
[13].
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