Anton Bovier, V\'eronique Gayrard, Pierre Picco
DISTRIBUTION OF OVERLAP PROFILES IN THE ONE-DIMENSIONAL KAC-HOPFIELD MODEL
(317K, PS)
ABSTRACT. We study a one-dimensional version of the Hopfield model with
long, but finite range interactions below the critical temperature.
In the thermodynamic limit we obtain large deviation estimates for the
distribution of the ``local'' overlaps, the range of the interaction,
$\gamma^{-1}$, being the large parameter. We show in particular that the
local overlaps in a typical Gibbs configuration are constant and equal to one
of the mean-field equilibrium values on a scale $o(\g^{-2})$. We also
give estimates on the size of typical ``jumps''. i.e. the regions where
transitions from one equilibrium value to another take place. Contrary to the
situation in the ferromagnetic Kac-model, the structure of the
profiles is found to be governed by the quenched disorder rather than
by entropy.