  We discuss first-order phase transitions that are broadened by disorder, but
still remain first order on the local mesoscopic level. Using vortex-matter as
our paradigm, we argue that phase transitions in general can be broadened by
two different causes viz. due to a distribution of the phase transition point
(field or temperature) from one region of the sample to another, or due to a
distribution in the local magnetic field experienced by different regions of
the sample. We show that in the second case there is an apparent "extrinsic"
hysteresis even if the transition is locally second-order. We show that bulk
measurements under isothermal conditions can be used to infer whether the
broadened transition is first-order at the local (mesoscopic) level.
  Keywords: vortex-matter, phase transitions, hysteresis
