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
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