Structural stability of the phase transition in Dicke-like models

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Abstract
The free energy for a general class of Dicke models is computed and expressed simply as the minimum value of a potential function Φ = (E−TS)/N. The function E/N is the image of the Hamiltonian under the quantum–classical correspondence effected by the atomic and field coherent state representations, and the function S is the logarithm of an SU(2) multiplicity factor. The structural stability of the second order phase transition under changes in the functional form of the Hamiltonian is determined by searching for stability changeovers along the thermal critical branch of Φ. The necessary condition for the presence of a second order phase transition is completely determined by the canonical kernel of the Hamiltonian. The sufficient condition is that a first order phase transition not occur at higher temperature. The critical temperature for a second order phase transition is given by a gap equation of Hepp–Lieb type.