  We establish the behavior of the energy of minimizers of non-local
Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near
the onset of multi-droplet patterns. Under suitable scaling of the background
charge density with vanishing surface tension the non-local Ginzburg-Landau
energy becomes asymptotically equivalent to a sharp interface energy with
screened Coulomb interaction. Near the onset the minimizers of the sharp
interface energy consist of nearly identical circular droplets of small size
separated by large distances. In the limit the droplets become uniformly
distributed throughout the domain. The precise asymptotic limits of the
bifurcation threshold, the minimal energy, the droplet radii, and the droplet
density are obtained.
