  We report results demonstrating a singularity in the hysteresis of magnetic
materials, the reversal-field memory effect. This effect creates a
nonanalyticity in the magnetization curves at a particular point related to the
history of the sample. The microscopic origin of the effect is associated with
a local spin-reversal symmetry of the underlying Hamiltonian. We show that the
presence or absence of reversal-field memory distinguishes two widely studied
models of spin glasses (random magnets).
