Residual Energies after Slow Cooling of Disordered Systems

The residual energy, ε(τ), left after cooling to zero temperature in a finite time τ is analyzed for various disordered systems, including spin-glasses and random-field magnets. We argue that the generic behavior for such frustrated systems is ε(τ)~(lnτ)^-ζ for large τ, with the exponent ζ depending on the system. This result is dominated in some cases by a distribution of classical two-level systems with low excitation energies, and in other cases by large-scale nonequilibrium effects.