  We consider two schematic models of glasses subjected to oscillatory shear
deformation, motivated by the observations, in computer simulations of a model
glass, of a nonequilibrium transition from a localized to a diffusive regime as
the shear amplitude is increased, and of persistent memory effects in the
localized regime. The first of these schematic models is the NK model, a spin
model with disordered multi-spin interactions previously studied as a model for
sheared amorphous solids. The second model, a transition matrix model, is an
abstract formulation of the manner in which occupancy of local energy minima
evolves under oscillatory deformation cycles. In both of these models, we find
a behavior similar to that of an atomic model glass studied earlier. We discuss
possible further extensions of the approaches outlined.
