Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-07-03
Phys. Rev. E, 62 (2000), 5721
Physics
Condensed Matter
Disordered Systems and Neural Networks
9 pages, 13 figures, minor typos corrected. To appear in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.62.5721
In this work we study numerically the out of equilibrium dynamics of the Hopfield model for associative memory inside its spin-glass phase. Besides its interest as a neural network model it can also be considered as a prototype of fully connected magnetic systems 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 work we analyse the two-time auto-correlation 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 ageing phenomena and presents features that suggest a non trivial breaking of replica symmetry.
Cannas Sergio A.
Montemurro Marcelo A.
Stariolo Daniel A.
Tamarit Francisco A.
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