  We prove, by means of a unified treatment, that the superradiant phase
transitions of Dicke and classical oscillator limits of simple light-matter
models are indeed of the same type. We show that the mean-field approximation
is exact in both cases, and compute the structure and location of the
transitions in parameter space. We extend this study to a fuller range of
models, paying special attention to symmetry considerations. We uncover general
features of the phase structure in the space of parameters of these models.
