  We discuss the finite size behavior of the adiabatic Dicke model, describing
the collective coupling of a set of N-two level atoms (qubits) to a faster
(electromagnetic) oscillator mode. The energy eigen-states of this system are
shown to be directly related to those of another widely studied collective spin
model, the uniaxial one. By employing an approximate continuum approach, we
obtain a complete characterization of the properties of the latter, which we
then use to evaluate the scaling properties of various observables for the
original Dicke model near its quantum phase transition.
