Hysteresis in isotropic spin systems

The authors consider hysteresis in isotropic N-vector models in d dimensions in an external spatially uniform field varying sinusoidally in time. They use renormalization group arguments to show that for d ) 2 and N >or= 2, for small frequencies omega , and small amplitudes H0 of the field, the area of the hysteresis loop scales as (H0 omega )12/. with logarithmic corrections. For N =1 and d ) 1, using nucleation theory they show that the area for omega << H0 scales as mod Tln(H0 omega ) mod -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.