  The melting of a polydisperse hard disk system is investigated by Monte Carlo
simulations in the semigrand canonical ensemble. This is done in the context of
possible continuous melting by a dislocation unbinding mechanism, as an
extension of the 2D hard disk melting problem. We find that while there is
pronounced fractionation in polydispersity, the apparent density-polydispersity
gap does not increase in width, contrary to 3D polydisperse hard spheres. The
point where the Young's modulus is low enough for the dislocation unbinding to
occur moves with the apparent melting point, but stays within the density gap,
just like for the monodisperse hard disk system. Additionally, we find that
throughout the accessible polydispersity range, the bound dislocation-pair
concentration is high enough to affect the dislocation unbinding melting as
predicted by Kosterlitz, Thouless, Halperin, Nelson and Young.
