COUPLED DYNAMICS OF FAST SPINS AND SLOW INTERACTIONS IN NEURAL NETWORKS AND SPIN SYSTEMS

We examine an Ising spin system in which both spins and the interactio ns between them may evolve in time, although on disparate timescales, such that the couplings change adiabatically. In thermal equilibrium w e find a novel application of the replica method, but for finite repli ca number, representing the ratio of the temperatures of the spin and interaction systems. Regimes where the motion of the couplings has non -trivial effects are found in addition to those where solely the stoch asticity of these interaction weights is significant, and this issue i s closely related to the orders of the transitions between the various phases observed. Simulation results lend support to the analysis.