  We investigate the thermodynamic properties of a field-induced supersolid
phase in a 2D quantum antiferromagnet model. Using quantum Monte Carlo
simulations, a very rich phase diagram is mapped out in the temperature -
magnetic field plane, with an extended supersolid region where a diagonal
(solid) order coexists with a finite XY spin stiffness (superfluid). The
various quantum and thermal transitions out of the supersolid state are
characterized. Experimental consequences in the context of field-induced
magnetization plateau materials are briefly discussed.
