  In the collective photon emission from atomic clouds both the atomic
transition frequency and the decay rate are modified compared to a single
isolated atom, leading to the effects of superradiance and subradiance. In this
Letter, we analyse the properties of the Euclidean random matrix associated to
the radiative dynamics of a cold atomic cloud, previously investigated in the
contexts of photon localization and Dicke super- and subradiance. We present
evidence of a new type of phase transition, surprisingly controlled by the
cooperativeness parameter, rather than the spatial density or the diagonal
disorder. The numerical results corroborate the occurrence of such a phase
transition at a critical value of the cooperativeness parameter, above which
the lower edge of the spectrum vanishes exhibiting a macroscopic accumulation
of eigenvalues. Independent evaluations based on the two phenomena provide the
same value of the critical cooperativeness parameter.
