  A general procedure is established to calculate the quantum phase diagrams
for finite matter-field Hamiltonian models. The minimum energy surface
associated to the different symmetries of the model is calculated as a function
of the matter-field coupling strengths. By means of the ground state wave
functions, one looks for minimal fidelity or maximal Bures distance surfaces in
terms of the parameters, and from them the critical regions of those surfaces
characterize the finite quantum phase transitions. Following this procedure for
$N_a=1$ and $N_a=4$ particles, the quantum phase diagrams are calculated for
the generalised Tavis-Cummings and Dicke models of 3-level systems interacting
dipolarly with $2$ modes of electromagnetic field. For $N_a=1$, the reduced
density matrix of the matter allows us to determine the phase regions in a
$2$-simplex (associated to a general three dimensional density matrix), on the
different $3$-level atomic configurations, together with a measurement of the
quantum correlations between the matter and field sectors. As the occupation
probabilities can be measured experimentally, the existence of a quantum phase
diagram for a finite system can be established.
