Out-of-equilibrium dynamics of the Hopfield model in its spin-glass phase

The off-equilibrium dynamics of the Hopfield model for associative memory inside its spin glass phase. By adjusting the ratio between the number of stored configurations and the total number of neurons, the phase space structure can be controlled and complexities from the simple mean-field ferromagnet to that of the Sherrington Kirkpatrick spin-glass model can be obtained. The two-time autocorrelation function, the magnetization decay and the distribution of overlaps between states are analyzed. Within the model spin-glass phase, the dynamics exhibits aging phenomena and presents features that suggest a nontrivial breaking of replica symmetry.