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We study the thermodynamic properties of the Hopfield model of an autoassociative memory. If N denotes the number of neurons and M(N) the number of stored patterns, we prove the following results: if M/N #arrow down# 0 as N #arrow up# #infinity#, then there extists an infinite number of infinite volume Gibbs measures for all temperatures T < 1 concentrated on spin configurations that have overlap with exactly one specific pattern. Moreover, the measures induced on the overlap parameters are Dirac measures concentrated on a single point. If M/N #-># #alpha#, as N #arrow up# #infinity# for #alpha# small enough, we show that for temperatures T smaller than some T(#alpha#)<1, the induced measures can have support only on a disjoint union of balls around the previous points, but we cannot construct the infinite volume measures through convergent sequences of measures. (orig.)SIGLEAvailable from TIB Hannover: RR 5549(79)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Topics:
12C - Applied mathematics, HOPFIELD MODEL: M, THERMODYNAMIC PROPERTIES, GIBBS MEASURES, DIRAC MEASURES, LAPLACE METHOD, DENSITY, GLOBAL MINIMA, RANDOM MATRIX

Year: 1994

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