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A deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential both to advance our fundamental physics understanding and to harness technological opportunities arising from optically controlled quantum many-body states. This paper provides a numerical study of dynamical phases and the transitions between them in the nonequilibrium steady state of the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. We demonstrate a nonthermal transition that is characterized by a qualitative change in the magnon distribution from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive. A finite-size analysis reveals static and dynamical critical scaling at the transition, with a discontinuous slope of the magnon number versus driving field strength and critical slowing down at the transition point. Implications for experiments on quantum materials and polariton condensates are discussed.
