  We study the counterion condensation on a two dimensional charged disc in the
limit of infinite dilution, and compare the energy-temperature relation
obtained from the canonical free energy and microcanonical entropy. The
microcanonical entropy is piecewise linear in energy, and is shown to be
concave for all energies. As a result, even though the interactions are
long-ranged, the energy-temperature relation and hence the counterion
condensation transition points are identical in both the ensembles.
