  Entanglement and quantum correlations between atoms are not usually
considered key ingredients of the superradiant phase transition. Here we
consider the Tavis-Cummings model, a solvable system of two-levels atoms,
coupled with a single-mode quantized electromagnetic field. This system
undergoes a superradiant phase transition, even in a finite-size framework,
accompanied by a spontaneous symmetry breaking, and an infinite sequence of
energy level crossings. We find approximated expressions for the ground state,
its energy, and the position of the level crossings, valid in the limit of a
very large number of photons with respect to that of the atoms. In that same
limit, we find that the number of photons scales quadratically with the
coupling strength, and linearly with the system size, providing a new insight
into the superradiance phenomenon. Resorting to novel multipartite measures, we
then demonstrate that this quantum phase transition is accompanied by a
crossover in the quantum correlations and entanglement between the atoms
(qubits). The latters therefore represent suited order parameters for this
transition. Finally, we show that these properties of the quantum phase
transition persist in the thermodynamic limit.
