  We introduce a class of hybrid quantum circuits, with random unitaries and
projective measurements, which host long-range order in the area law
entanglement phase of the steady state. Our primary example is circuits with
unitaries respecting a global Ising symmetry and two competing types of
measurements. The phase diagram has an area law phase with spin glass order,
which undergoes a direct transition to a paramagnetic phase with volume law
entanglement, as well as a critical regime. Using mutual information
diagnostics, we find that such entanglement transitions preserving a global
symmetry are in new universality classes. We analyze generalizations of such
hybrid circuits to higher dimensions, which allow for coexistence of order and
volume law entanglement, as well as topological order without any symmetry
restrictions.
