ON THE OUT-OF-EQUILIBRIUM ORDER-PARAMETER IN LONG-RANGE SPIN-GLASSES

We show that the dynamical order parameters can be re-expressed in ter ms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirkpatrick model at long times. The resu lts suggest that the landscape this model visits at different long tim es in an out-of-equilibrium relaxation process is, in a sense, self-si milar. Furthermore, there is a similarity between the landscape seen o ut of equilibrium at long times and the equilibrium landscape. The cal culation is greatly simplified by making use of the superspace notatio n in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approac hes. We also perform numerical simulations which show good agreement w ith the analytical results for the out of equilibrium dynamics.