  We apply the Gaussian trajectories approach to the study of the critical
behavior of two-dimensional dissipative arrays of nonlinear photonic cavities,
in presence of two-photon driving and in regimes of sizable loss rates. In
spite of the highly mixed character of the density matrix of this system, the
numerical approach is able to provide precise estimations of the steady-state
expectation values, even for large lattices made of more than 100 sites. By
performing a finite-size scaling of the relevant properties of the steady
state, we extrapolate the behavior of the system in the thermodynamic limit and
we show the emergence of a second-order dissipative phase transition, belonging
to the universality class of thermal Ising model. This result indicates the
occurrence of a crossover when the loss rate is increased from the weak-loss
limit, in which the phase transition belongs to the universality class of the
quantum Ising model
