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^-ν below T_c, with an exponent which decreases continuously with temperature, ν(T)=12-π^-1(1-TT_c)+O((1-TT_c)²), in disagreement with previous predictions (ν=12).