Spin-glass models of a neural network

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Abstract
A general theory of spin-glass-like neural networks with a Monte Carlo dynamics and finitely many attractors (stored patterns) is presented. The long-time behavior of these models is determined by the equilibrium statistical mechanics of certain infinite-range Ising spin glasses, whose thermodynamic stability is analyzed in detail. As special cases we consider the Hopfield and the Little model and show that the free energy of the latter is twice that of the former because of a duplication of spin variables which occurs in the Little model. It is also indicated how metastable states can be partly suppressed or even completely avoided.