  Hysteresis is studied in a disordered Ising model in which diffusion of
antiferromagnetic bonds is allowed in addition to spin flips. Saturation
behavior changes to a figure-eight loop when diffusion is introduced. The upper
and lower fields delimiting the figure-eight are determined by the Hamiltonian,
while its surface and the crossing point depend on the temperature and details
of the dynamics. The main avalanche is associated with the disappearance of
hidden order. Some experimental observations of figure-eight anomalies are
discussed. It is argued they are a signal of a transient rearrangement of
domain couplings, characteristic of amorphous and/or magnetically soft samples,
and similar to evolution of kinetic glasses.
