Role of initial conditions in spin glass dynamics and significance of Parisi's q(x)

The authors argue that standard treatments of dynamics are incorrect for non-ergodic systems such as the Sherrington-Kirkpatrick model of a spin glass. Since the system never loses the memory of its initial state it is necessary to average over initial states with a Boltzmann weight to obtain time-dependent correlation functions as conventionally defined. It is now necessary to introduce replicas. The 'dynamical' order parameter, qEA, is equal to q(x=1) in Parisi's scheme whereas the statistical mechanics order parameter, q, is given by integral 0Iq(x) dx. They also propose an interpretation of the function q(x).