Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model

Abstract

We study the nonequilibrium relaxation of the spherical spin-glass model with p-spin interactions in the N\ensuremath{\rightarrow}\ensuremath{\infty} limit. We analytically solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynamic limit the system exhibits ``weak'' (as well as ``true'') ergodicity breaking and aging effects. We determine a functional Parisi-like order parameter ${\mathit{P}}_{\mathit{d}}$(q) which plays a similar role for the dynamics to that played by the usual function for the statics.