  We investigate the dynamics of two-dimensional quantum spin systems under the
combined effect of random unitary gates and local projective measurements. When
considering steady states, a measurement-induced transition occurs between two
distinct dynamical phases, one characterized by a volume-law scaling of
entanglement entropy, the other by an area-law. Employing stabilizer states and
Clifford random unitary gates, we numerically investigate square lattices of
linear dimension up to $L=48$ for two distinct measurement protocols. For both
protocols, we observe a transition point where the dominant contribution in the
entanglement entropy displays multiplicative logarithmic violations to the
area-law. We obtain estimates of the correlation length critical exponent at
the percent level; these estimates suggest universal behavior, and are
incompatible with the universality class of 3D percolation.
