  The critical value of the atom-field coupling strength for a finite number of
atoms is deter- mined by means of both, semiclassical and exact solutions. In
the semiclassical approach we use a variational procedure with coherent and
symmetry-adapted states, while for the exact quantum solution the concept of
fidelity is employed. These procedures allow for the determination of the phase
transitions in the model, and coincide in the thermodynamic limit. For the
three cases men- tioned above, universal parametric curves are obtained for the
expectation values of both the first quadrature of the electromagnetic field,
and the atomic relative population, as implicit functions of the atom-field
coupling parameter, valid for the ground- and first-excited states.
