96-45 Bleher P., Ruiz J., Zagrebnov V.

One-Dimensional Random Field Ising Model: Gibbs States and Structure of Ground States (46K, LateX) Feb 19, 96

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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.

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