Dynamic Theory of the Spin-Glass Phase

Exact averaged equations for spin relaxation in infinite-ranged spin-glasses are derived. It is shown that, in general, time-persistent terms in both correlation and response functions cannot be treated as purely static order parameters. A dynamic stability criterion for static solutions is derived. In the marginally stable solution dynamic correlations decay algebraically t- below Tc, with an exponent which decreases continuously with temperature, (T)=12-1(1-TTc)+O((1-TTc)2), in disagreement with previous predictions (=12).