  We investigate the influence of critical phenomena on two distinct physical
processes: the center-of-mass decoherence of a single emitter, and the
collective radiation of two emitters. We address these different physical
mechanisms with an unified formalism relying on standard perturbation theory.
We decompose the decoherence and the collective emission rates as a sum of two
contributions, accounting for the spontaneous emission and for interference
effects respectively. The former is enhanced by the Purcell effect when the
material is in the vicinity of the emitter(s). The latter, associated to
quantum interferences, experiences a "sudden death" near the critical point of
the phase transition. Our findings unveil the interplay between the Purcell and
collective effects and its dependence on metal-insulator transitions. We
discuss two specific examples of phase transitions: the percolation transition
in a metal-dielectric composite, and the metal-insulator transition in VO2. In
the latter, decoherence and collective emission rates exhibit a characteristic
hysteresis that strongly depends on the material temperature. These results,
based on experimental data, suggest that VO2 could be explored as a versatile
material platform where decoherence and collective emission can be tuned by
varying the temperature.
