Residual energies after slow cooling of disordered systems.

The residual energy epsilon(tau), left after cooling to zero temperature in a finite time tau is analyzed for various disordered systems, including spin glasses and random-field magnets. We argue that the generic behavior for such frustrated systems is epsilon(tau) ~ (lntau)(-iota) for large tau. 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 non-equilibrium effects. A recent conjecture that there is a direct connection between the behavior of epsilon (tau) and the algorthrmic complexity of finding the system's ground state is shown to be false.