Metastates in the Hopfield model in the replica symmetric regime

Anton Bovier & Véronique Gayrard
We study the finite dimensional marginals of the Gibbs measure in the Hopfield model at low temperature when the number of patterns, M, is proportional to the volume with a sufficiently small proportionality constant ɑ > 0. It is shown that even when a single pattern is selected (by a magnetic field or by conditioning), the marginals do not converge almost surely, but only in law. The corresponding limiting law is constructed explicitly. We fit...
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