  Two-level atoms interacting with a one mode cavity field at zero temperature
have order parameters which reflect the presence of a quantum phase transition
at a critical value of the atom-cavity coupling strength. Two popular examples
are the number of photons inside the cavity and the number of excited atoms.
Coherent states provide a mean field description, which becomes exact in the
thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states
(SACS) the critical behavior can be described for a finite number of atoms. A
variation after projection treatment, involving a numerical minimization of the
SA energy surface, associates the finite number phase transition with a
discontinuity in the order parameters, which originates from a competition
between two local minima in the SA energy surface.
