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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.
In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which
We find a dynamic effect in the non-equilibrium dynamics of a spin glass that closely parallels equilibrium temperature chaos. This effect, that we name dynamic temperature chaos, is spatially heterogeneous to a large degree. The key controlling quan
We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures
We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting fiel
We study the phase transition of the $pm J$ Heisenberg model in three dimensions. Using a dynamical simulation method that removes a drift of the system, the existence of the spin-glass (SG) phase at low temperatures is suggested. The transition temp