  We investigate the influence of the driving mechanism on the hysteretic
response of systems with athermal dynamics. In the framework of local-mean
field theory at finite temperature (but neglecting thermallly activated
processes), we compare the rate-independent hysteresis loops obtained in the
random field Ising model (RFIM) when controlling either the external magnetic
field $H$ or the extensive magnetization $M$. Two distinct behaviors are
observed, depending on disorder strength. At large disorder, the $H$-driven and
$M$-driven protocols yield identical hysteresis loops in the thermodynamic
limit. At low disorder, when the $H$-driven magnetization curve is
discontinuous (due to the presence of a macroscopic avalanche), the $M$-driven
loop is re-entrant while the induced field exhibits strong intermittent
fluctuations and is only weakly self-averaging. The relevance of these results
to the experimental observations in ferromagnetic materials, shape memory
alloys, and other disordered systems is discussed.
