  Collective phenomena in the Tavis-Cummings model has been widely studied,
focusing on the phase transition features. In many occasions, it has been used
variational approaches that consider separated radiation-matters systems. In
this paper, we examine the role of the quantum entanglement of an assembly of
two-level emitters coupled to a single-mode cavity; this allows us to
characterise the quantum correlated state for each regime. Statistical
properties of the system, e.g., the first four statistical moments, show
clearly the structure of the light and matter distributions. Even though the
second order correlation function goes to one in some regimes, the statistical
analysis evidence a sharp departure from coherent behaviour, contrarily to the
common understanding.
