  Hysteresis in cycling through first-order phase transitions in vortex matter,
akin to the well-studied phenomenon of supercooling of water, has been
discussed in literature. Hysteresis can be seen while varying either
temperature T or magnetic field H (and thus the density of vortices). Our
recent work on phase transitions with two control variables shows that the
observable region of metastability of the supercooled phase would depend on the
path followed in H-T space, and will be larger when T is lowered at constant H
compared to the case when H is lowered at constant T. We discuss the effect of
isothermal field variations on metastable supercooled states produced by
field-cooling. This path dependence is not a priori applicable to metastability
caused by reduced diffusivity or hindered kinetics.
