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We investigate the thermodynamic properties of a field-induced supersolidphase in a 2D quantum antiferromagnet model. Using quantum Monte Carlosimulations, 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). Thevarious quantum and thermal transitions out of the supersolid state arecharacterized. Experimental consequences in the context of field-inducedmagnetization plateau materials are briefly discussed.Comment: To appear in Phys. Rev. Let

Quantum and Thermal Transitions Out of the Supersolid Phase of a 2D Quantum Antiferromagnet