  Using Monte Carlo simulations, we systematically investigate the effect of
particle size distribution on the phase behaviour of polydisperse hard disks.
Compared with the commonly used Gaussian-like polydisperse hard disks [Commun.
Phys. 2, 70 (2019)], we find that the phase behaviour of polydisperse hard-disk
systems with lognormal and triangle distributions are significantly different.
In polydisperse hard-disk systems of lognormal distributions, although the
phase diagram appears similar to that of Gaussian-like polydisperse hard disks,
the re-entrant melting of hexatic or solid phase can not be observed in
sedimentation experiments. For polydisperse hard-disk systems of triangle
distributions, the phase behaviour is qualitatively different from the
Gaussian-like and lognormal distributions, and we can not reach any system of
true polydispersity larger than 0.06, which is due to the special shape of the
triangle distribution. Our results suggest that the exact particle size
distribution is of primary importance in determining the phase behaviour of
polydisperse hard disks, and we do not have a universal phase diagram for
different polydisperse hard-disk systems.
