Possibility of Kauzmann points in the vortex matter phase diagram of single crystal YBa$_2$Cu$_3$O$_{7-\delta}$
We highlight interesting thermomagnetic history effects across the transition line between the (quasi) ordered and disordered vortex states in single crystal YBa$_2$Cu$_3$O$_{7-\delta}$, and argue that these features are indicative of the first order nature of the transition line. We suggest that the destruction of the ordered vortex state in YBa$_2$Cu$_3$O$_{7-\delta}$ leading to vortex liquid (at high temperatures and low fields) and amorphous vortex solid (at low temperatures and high fields), takes place along a unified first-order transition line. The nonmonotonic behavior of this first order transition line gives rise to the possibility of more than one Kauzmann point where the entropies of the ordered and disordered vortex states are equal. In the high temperature region, one may order the vortex lattice by warming it, giving rise to an inverse melting effect.