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

• Autor(a) principal: Montemurro, Marcelo A.
• Data de Publicação: 2000
• Outros Autores: Tamarit, Francisco A., Stariolo, Daniel Adrian, Cannas, Sergio A.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/103662
• topic: Fenomenos criticos; Ferromagnetismo; Magnetização; Vidros de spin

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.