  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.
