Reversibility and Irreversibility in Spin-Glasses: The Free-Energy Surface

The free-energy surface of a mean-field model for a spin-glass in a field $H$ is studied numerically. Field-cooled (FC) and zero-FC magnetizations are obtained that look qualitatively like experiment. The FC state is shown to satisfy Maxwell's relations. Changing $H$ below $T_g$ generally leads to irreversible behavior. In the absence of relaxation effects, it is found that all processes obtained upon cooling are reversible. New hysteresis effects are predicted.