Critical hysteresis in random-field XY and Heisenberg models.

We study zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. We consider three distributions of the random field and present exact solutions in the mean-field limit. The results show a strong effect of the form of disorder on critical hysteresis as well as the shape of hysteresis loops. A discrepancy with an earlier study based on the renormalization group is resolved.