Finite-size behavior of quantum collective spin systems

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 eigenstates 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.