Self-organized criticality in the hysteresis of the Sherrington-Kirkpatrick model

We study hysteretic phenomena in random ferromagnets. We argue that the ang le-dependent magnetostatic (dipolar) terms introduce frustration and long-r ange interactions in these systems. This makes it plausible that the Sherri ngton-Kirkpatrick model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations and large scale numerical simulations to characterize the hysteresis of the zero tem perature SK model. By constructing the distribution functions of the avalan che sizes, magnetization jumps and local fields, we conclude that the syste m exhibits self-organized criticality everywhere on the hysteresis loop. (C ) 2000 Elsevier Science B.V. All rights reserved.