On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model

TLDR: In this paper, the authors derived analytical results for the long-time relaxation of the Sherrington-Kirkpatrick model, starting from a random configuration, and showed that the system never achieves local equilibrium in any fixed sector of phase space, but remains in an asymptotic out-of-equilibrium regime.

Abstract: Starting from a set of assumptions on the long-time limit behaviour of the nonequilibrium relaxation of mean-field models in the thermodynamic limit, we derive analytical results for the long-time relaxation of the Sherrington-Kirkpatrick model, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of phase space, but remains in an asymptotic out-of-equilibrium regime. We clearly state and motivate the assumptions made. For the study of the out-of-equilibrium dynamics of spin-glass models, we propose as a tool, both numerical and analytical, the use of 'triangle relations' which describe the geometry of the configurations at three (long) different times.