  Utilizing large-scale Monte-Carlo simulations, we investigate an
unconventional two-component classical plasma in two dimensions which controls
the behavior of the norms and overlaps of the quantum-mechanical wavefunctions
of Ising-type quantum Hall states. The plasma differs fundamentally from that
which is associated with the two-dimensional XY model and Abelian fractional
quantum Hall states. We find that this unconventional plasma undergoes a
Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal.
The parameter values corresponding to Ising-type quantum Hall states lie on the
metallic side of this transition. This result verifies the required properties
of the unconventional plasma used to demonstrate that Ising-type quantum Hall
states possess quasiparticles with non-Abelian braiding statistics.
