 9631 Anton Bovier, V\'eronique Gayrard, Pierre Picco
 DISTRIBUTION OF OVERLAP PROFILES IN THE ONEDIMENSIONAL KACHOPFIELD MODEL
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Feb 2, 96

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Abstract. We study a onedimensional 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 meanfield 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 Kacmodel, the structure of the
profiles is found to be governed by the quenched disorder rather than
by entropy.
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