Hysteresis in vortex glass transitions of the first order

The distribution of relaxation times in a glass is very broad. As a result the free energy of a glass slowly approaches its equilibrium value but never reaches it. This slow relaxation explains why, in the hysteresis cycle, the melting tempetature is higher than the solidification temperature.

We estimate the width of this hysteresis for a general type of transition into the glassy state. We apply these estimates to the special case of the vortex melting transition and find good agreement with recent experiments. We show how strong disorder changes the character of the vortex melting transition and evaluate the position of the tricritical point.