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The free energy of a class of Hopfield models
Authors:M Shcherbina  B Tirozzi
Institution:(1) Institute of Low Temperature Physics and Engineering, 310164 Kharkov, Ukraine;(2) Department of Mathematics, University of Rome ldquoLa Sapienza,rdquo, 00185 Rome, Italy
Abstract:We show that in the limitprarr infin,N rarr 0,agr=p/N rarr 0 the limit free energy of the Hopfield model equals in probability the Curie-Weiss free energy. We prove also that the free energy of the Hopfield model is self-averaging for any finite infin.
Keywords:Free energy  overlaps  self-averaging
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