Liu hard disk equation of state

The Liu equation of state for hard disks (2-dimensional hard spheres) is given by Eq. 1 of .

For the stable fluid:

$Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2}$

where the packing fraction is given by $\eta = \pi \rho \sigma^2 /4$ where $\sigma$ is the diameter of the disks.

The EoS for the stable fluid, liquid-hexatic transition region and hexatic:

$Z_h = Z_v + \frac{b_1 \eta^m_1 + b_2 \eta^m_2}{(1-c \eta)}$