Statistical Physics and Spin Glasses

Abstract

We have learned in Part I that there is a complete analogy between neural networks having symmetric synaptic efficacies w _ij and a certain type of magnetic system characterized by a lattice of discrete spin variables s _i = ±1. Such systems are known under the name Ising system. If the spin—spin interaction, i.e. the coupling coefficients w _ij , extend over large distances and take on irregular values one speaks of a spin glass. The peculiar properties of such spin glasses have caught the attention of physicists and have been studied closely during the last decade. In the following chapters we will make ample use of the results and the methods developed in the course of these investigations. Despite the dose magnetic analogy, however, we will always keep in mind that we intend to describe neural networks.