Residual energies after slow cooling of disordered systems

The residual energy, μ, left after cooling to zero temperature in a finite time is analyzed for various disordered systems, including spin-glasses and random-field magnets. We argue that the generic behavior for such frustrated systems is μ for large, with the exponent 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.