Journal of Statistical Physics. Vol. 84. Nos. 5/6, 1996. p. 1077-1093.
We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibbs state is
unique for any realization of the external field. Then we prove that as T->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.