Distribution of overlap profiles in the one-dimensional Kac-Hopfield model

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.

64pp, Plain TeX

References in corpus (1)

• The Retrieval Phase of the Hopfield Model: A Rigorous Analysis of the Overlap Distribution

Cited by in corpus (2)

• Finite-range spin glasses in the Kac limit: free energy and local observables
• The low-temperature phase of Kac-Ising models