  The full Dicke model describes a system of $N$ identical two level-atoms
coupled to a single-mode quantized bosonic field. The model considers rotating
and counter-rotating coupling terms between the atoms and the bosonic field,
with coupling constants $g_1$ and $g_2$, for each one of the coupling terms,
respectively. We study finite temperature properties of the model using the
path integral approach and functional methods. In the thermodynamic limit,
$N\rightarrow\infty$, the system exhibits phase transition from normal to
superradiant phase, at some critical values of temperature and coupling
constants. We distinguish between three particular cases, the first one
corresponds to the case of rotating wave approximation, which $g_1\neq 0$ and
$g_2=0$, the second one corresponds to the case of $g_1=0$ and $g_2\neq 0$, in
these two cases the model has a continuous symmetry. The last one, corresponds
to the case of $g_1\neq 0$ and $g_2\neq 0$, which the model has a discrete
symmetry. The phase transition in each case is related to the spontaneous
breaking of its respective symmetry. For each one of these three particular
cases, we find the asymptotic behaviour of the partition function in the
thermodynamic limit, and the collective spectrum of the system in the normal
and the superradiat phase. For the case of rotating wave approximation, and
also the case of $g_1=0$ and $g_2\neq 0$, in the superradiant phase, the
collective spectrum has a zero energy value, corresponding to the Goldstone
mode associated to the continuous symmetry breaking of the model. Our analyse
and results are valid in the limit of zero temperature,
$\beta\rightarrow\infty$, in which, the model exhibits a quantum phase
transition.
