  Motivated by recent experiments reporting Bose-Einstein condensation (BEC) of
light coupled to incoherent dye molecules in a microcavity, we show that due to
a dimensionality mismatch between the 2D cavity-photons and the 3D arrangement
of molecules, the relevant molecular degrees of freedom are collective Dicke
states rather than individual excitations. For sufficiently high dye
concentration the coupling of the Dicke states with light will dominate over
local decoherence. This system also shows Mott criticality despite the absence
of an underlying lattice in the limit when all dye molecules become excited.
