  We present a theoretical study of a Berezinskii-Kosterlitz-Thouless like
phase transition in lattices of nonequilibrium photon condensates. Starting
from linearized fluctuation theory and the properties of vortices, we propose
an analytical formula for the critical point containing four fitting
parameters, that captures well all our numerical simulations. We find that the
ordered phase becomes more stable when driving and dissipation is increased.
