Memory Effects in Schematic Models of Glasses Subjected to Oscillatory Deformation

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.