Ising-spin neural networks with spatial structure

Abstract

We study Ising spin models for neural networks with spatial structure, in which patterns are stored according to Hebb's rule. From the microscopic dynamics given by the master equation we derive a partial differential equation for the position- and time-dependent correlations between the system state and the stored patterns. This equation can be used to study networks with finite range connections (not necessarily symmetric), the behaviour of domain boundaries and information transport. For systems with finite range connections we can compute the range of macroscopic order.