  We study the non-equilibrium steady state (NESS) of a driven dissipative
one-dimensional system near a critical point, and explore how the quantum
correlations compare to the known critical behavior in the ground state. The
model we study corresponds to a cavity array driven parametrically at a two
photon resonance, equivalent in a rotating frame to a transverse field
anisotropic XY model [C. E. Bardyn and A. Imamo\u{g}lu, Phys. Rev. Lett {\bf
109} 253606 (2012)]. Depending on the sign of transverse field, the steady
state of the open system can be either related to the ground state or to the
maximum energy state. In both cases, many properties of the entanglement are
similar to the ground state, although no critical behavior occurs. As one
varies from the Ising limit to the isotropic XY limit, entanglement range
grows. The isotropic limit of the NESS is however singular, with simultaneously
diverging range and vanishing magnitude of entanglement. This singular limiting
behavior is quite distinct from the ground state behavior, it can however be
understood analytically within spin-wave theory.
