Dynamical replica theory for disordered spin systems

We present a method to solve the dynamics of disordered spin systems on finite time scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical replica theory which, in the case of detailed balance, incorporates equilibrium replica theory as a stationary state. The theory is exact in various limits. We apply our theory to both the symmetric and the nonsymmetric Sherrington-Kirkpatrick spin glass, and show that it describes the (numerical) experiments very well. {} 1996 The American Physical Society.