Analysis of the ordering transition of hard disks through the Mayer   cluster expansion
  The available virial coefficients for the 2D hard disks model are transformed into a matrix representation of the thermodynamic potentials, which allows for an accurate description of the whole fluid phase, up to the phase transition. We find that the fluid phase terminates at the transition point, supporting the Kosterlitz-Thouless-Halperin-Nelson-Young picture of a second order phase transition into a Hexatic phase. The density and pressure at the transition are calculated from the available first ten virial coefficients, and are found to be in excellent agreement with recent Monte-Carlo calculations. Finally, we calculate the equation of state in the critical region. 
Eli Eisenberg and Asher Baram