HYSTERESIS IN ISOTROPIC SPIN SYSTEMS

We consider hysteresis in isotropic N-vector models in d dimensions in an external spatially uniform field varying sinusoidally in time. We use renormalization group arguments to show that for d > 2 and N greater-than-or-equal-to 2, for small frequencies omega, and small amplitudes H-0 of the field, the area of the hysteresis loop scales as (H-0omega)1/2 with logarithmic corrections. For N = 1 and d > 1, using nucleation theory we show that the area for omega much less than H-0 scales as \T ln(H-0omega)\-1/(d-1). The power-law dependence of the area of hysteresis loops in continuous spin systems is a manifestation of their self-organized criticality.