- 96-45 Bleher P., Ruiz J., Zagrebnov V.
- One-Dimensional Random Field Ising Model:
Gibbs States and Structure of Ground States
Feb 19, 96
(auto. generated ps),
of related papers
Abstract. We consider the random Gibbs field formalism for the ferromagnetic
random field Ising model as the simplest example of quenched
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.