Bleher P., Ruiz J., Zagrebnov V.
One-Dimensional Random Field Ising Model:
Gibbs States and Structure of Ground States
(46K, LateX)

ABSTRACT.  We consider the random Gibbs field formalism for the ferromagnetic
$1$-$D$ dichotomous
random field Ising model as the simplest example of quenched
disordered systems.
We prove that for non--zero temperatures the Gibbs state is unique
for any realization of the external field. Then we prove that as
$T\to 0$, the Gibbs state converges to a limit, a ground state,
for almost all realizations of the external field. The ground state
turns out to be a probability measure
concentrated on an infinite set of configurations,
and we give a constructive description of this measure.