  The effect of spatial correlations on the Purcell effect in a bidimensional
dispersion of resonant nanoparticles is analyzed. We perform extensive
calculations on the fluorescence decay rate of a point emitter embedded in a
system of nanoparticles statistically distributed according to a simple 2D
lattice-gas model near the critical point. For short-range correlations (high
temperature thermalization) the Purcell factors present a long-tailed statistic
which evolves towards a bimodal distribution when approaching the critical
point where the spatial correlation length diverges. Our results suggest
long-range correlations as a possible origin of the large fluctuations of
experimental decay rates in disordered metal films.
