  We prove the existence of non-trivial global minimizers of a class of free
energies related to aggregation equations with degenerate diffusion on
$\Real^d$. Such equations arise in mathematical biology as models for organism
group dynamics which account for competition between the tendency to aggregate
into groups and nonlinear diffusion to avoid over-crowding. The existence of
non-zero optimal free energy stationary solutions representing coherent groups
in $\Real^d$ is therefore of interest. The primary contribution is the
investigation of a notion of criticality associated with the global minimizer
problem. The notion arises from the scaling of diffusive and aggregative forces
as mass spreads and is shown to dictate the existence, and sometimes
non-existence, of global minimizers.
