Hysteresis and self-organized criticality in the O(N) model in the limit N to infinity

The authors consider the response of the ferromagnetic N-vector model to a sinusoidally varying external magnetic field in the large-N limit. In all dimensions d>2, they show that at low frequencies omega , and small amplitudes H0 of the field, the area of the hysteresis loop scales as (H0 omega )1/2 with logarithmic corrections. At very high frequencies, the area varies as H02/ omega . They find that for any H0 there is a dynamical phase transition separating these two frequency regimes. They determine numerically the critical frequency as a function of the field strength. In the high-frequency phase the magnetization is predominantly transverse to the external magnetic field.