Dynamic Theory of the Spin-Glass Phase

Abstract

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 $\sim t^{-\nu }$ below $T_c$, with an exponent which decreases continuously with temperature, $\nu \mathrm{}\left(T\right)=\frac{1}{2}-{\pi }^{-1\mathrm{}}\left(\frac{1-T}{T_c}\right)+O\left({\left(\frac{1-T}{T_c}\right)}^2\right)$, in disagreement with previous predictions ($\nu =\frac{1}{2}$).