LAUSR

We prove that superradiant phase transitions (SPTs) of the Dicke model and its generalizations in the thermodynamic and classical oscillator limit are indeed of the same type. In this sense, we unify SPTs under both limits at zero and finite temperature. We show that the mean-field approximation for bosons is exact in both cases, and compute the structure and location of the phase transitions in parameter space using a concise analytic method. Moreover, we illustrate how SPT properties (first order, second order, or none) are related to symmetry. Finally, we uncover general features of the phase structure in the space of parameters of these models with dipolar couplings. There will be a region of normal phase in the neighborhood of the origin of the space of dipolar couplings $\stackrel{P\vec}{\ensuremath{\gamma}}$, and that generally one flows radially in this space to a superradiant phase.