  In analogy with equilibrium phase transitions, we address the problem of the
instability to symmetry-breaking perturbations of systems undergoing a laser
transition. The symmetry in question is the $U(1)$ invariance with respect to a
phase factor, and the perturbation is a coherent field $E$, coupled to the
exciton. At the rate equation level we analyze first the case of a cavity
containing a single, two-level emitter, and then a chain of such cavities
interacting by photon hopping processes. In both cases spontaneous symmetry
breaking takes place when the system is in the lasing phase. For the laser
transition, the analogue of the thermodynamic limit is the scaling limit of
vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, so
that $g^2/\kappa$ remains finite. We show that in the lasing regime anomalous
averages persist in the $E \to 0$ limit, provided that the scaling limit is
performed first. Lasing diagnosis based on robust anomalous averages is
compared numerically with the familiar coherence criterion $g^{(2)}(0)=1$, and
the advantages of the former are discussed.
