ABSTRACT
This chapter shows that the memorization capacities of the Hopfield model can be "exactly" predicted using the statistical physics approach. The physics of magnetic media leads to several simple generalizations of ferromagnetism. An energy function can be associated with each configuration. The existence of an energy function is a result of the internal symmetries of the system: the dynamical equations are invariant with respect to translation in time and the interactions between particles obey the principle of equal action and reaction. At low temperatures, the arguments of the exponentials are large in absolute value, and the probabilities of low energy configurations are correspondingly much higher than the probabilities of high energy configurations. Taking the temperature into account in a dynamical system is reflected in the probabilistic nature of the changes of state of its components. These components are no longer described by deterministic automata, but by probabilistic automata.
