Abstract
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 Gibb state is unique for any realization of the external field. Then we prove that asT→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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Bleher, P.M., Ruiz, J. & Zagrebnov, V.A. One-dimensional random-field ising model: Gibbs states and structure of ground states. J Stat Phys 84, 1077–1093 (1996). https://doi.org/10.1007/BF02174129
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DOI: https://doi.org/10.1007/BF02174129