Liu hard disk equation of state

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

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

The global EoS for all phases: \eta >= 0.72