ANALYTICAL SOLUTION OF THE OFF-EQUILIBRIUM DYNAMICS OF A LONG-RANGE SPIN-GLASS MODEL

We study the nonequilibrium relaxation of the spherical spin-glass mod el with p-spin interactions in the N --> infinity limit. We analytical ly solve the asymptotics of the magnetization and the correlation and response functions for long but finite times. Even in the thermodynami c limit the system exhibits ''weak'' (as well as ''true'') ergodicity breaking and aging effects. We determine a functional Parisi-like orde r parameter P(d)(q) which plays a similar role for the dynamics to tha t played by the usual function for the statics.