ORDER-PARAMETER FLOW IN THE FULLY CONNECTED HOPFIELD MODEL NEAR SATURATION

We present an exact dynamical theory, valid on finite time scales, to describe the fully connected Hopfield model near saturation in terms o f deterministic flow equations for order parameters. Two transparent a ssumptions allow us to perform a replica calculation of the distributi on of intrinsic-noise components of the alignment fields. Numerical si mulations support our assumptions and indicate that our equations desc ribe the shape of the intrinsic-noise distribution and the macroscopic dynamics correctly in the region where replica symmetry is stable. In equilibrium our theory reproduces the saddle-point equations obtained in the thermodynamic analysis by Amit, Gutfreund, and Sompolinsky [Ph ys. Rev. A 32, 1007 (1985); Phys. Rev. Lett. 55, 1530 (1985)], the onl y difference being the absence in the present formalism of negative en tropies at low temperatures.