Abstract
We prove that in the ergodic region [T>J 2(1 + rα)] the deviation of the total free energy of the Hopfield neural network converges in distribution asN → ∞ to a (shifted) Gaussian variable. Moreover, the free energy per site converges in probability to lim(1/N)ln≪ℤ N ≫.
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Scacciatelli, E., Tirozzi, B. Fluctuation of the free energy in the Hopfield model. J Stat Phys 67, 981–1008 (1992). https://doi.org/10.1007/BF01049007
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DOI: https://doi.org/10.1007/BF01049007