 9645 Bleher P., Ruiz J., Zagrebnov V.
 OneDimensional 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 nonzero 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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