To harness technological opportunities arising from optically controlled quantum many-body states a deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential. Here we provide numerical evidence for a dynamical phase transition in the nonequilibrium steady state of interacting magnons in the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. This nonthermal transition 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, 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.
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