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

Montemurro, Marcelo A.; Tamarit, Francisco A.; Stariolo, Daniel A. and Cannas, Sergio A. (2000). Out-of-equilibrium dynamics of the Hopfield model in its spin-glass phase. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 62(4 B) pp. 5721–5728.

DOI: https://doi.org/10.1103/PhysRevE.62.5721


In this paper, we study numerically the out-of-equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Aside from its interest as a neural network model, it can also be considered as a prototype of a fully connected magnetic system with randomness and frustration. By adjusting the ratio between the number of stored configurations p and the total number of neurons N, one can control the phase-space structure, whose complexity can vary between the simple mean-field ferromagnet (when p=1) and that of the Sherrington Kirkpatrick spin-glass model (for a properly taken limit of an infinite number of patterns). In particular, little attention has been devoted to the spin-glass phase of this model. In this paper, we analyze the two-time autocorrelation function, the decay of the magnetization and the distribution of overlaps between states. The results show that within the spin-glass phase of the model, the dynamics exhibits aging phenomena and presents features that suggest a non trivial breaking of replica symmetry.

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