HYSTERESIS AND SELF-ORGANIZED CRITICALITY IN THE O(N) MODEL IN THE LIMIT N -]INFINITY

We 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, we show that at low frequencies omega, and small amplitudes H0 of the field, the area of the hysteresis loop scales as (H0omega)1/2 with logarithmic corrections. At very high frequencies, the area varies as H02/omega. We find that for any H0 there is a dynamical phase transition separating these two frequency regimes. We 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.