  Because of long-wavelength fluctuations, the nature of solids and phase
transitions in 2D are different from those in 3D systems, and have been heavily
debated in past decades, in which the focus was on the existence of hexatic
phase. Here, by using large scale computer simulations, we investigate the
melting transition in 2D systems of polydisperse hard disks. We find that, with
increasing the particle size polydispersity, the melting transition can be
qualitatively changed from the recently proposed two-stage process to the
Kosterlitz-Thouless-Halperin-Nelson-Young scenario with significantly enlarged
stability range for hexatic phase. Moreover, re-entrant melting transitions are
found in high density systems of polydisperse hard disks, which were proven
impossible in 3D polydisperse hard-sphere systems. These suggest a new
fundamental difference between phase transitions in polydisperse systems in 2D
and 3D.
