Alder-Hoover-Young hard disk equation of state

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The Alder-Hoover-Young hard disk equation of state is given by (Ref. 1 Eq. 1)

Z = \frac{pV}{Nk_BT} = \frac{D}{\alpha}+ C_0 + C_1\alpha

where Z is the compressibility factor, C_0 = 1.90 \pm 0.01 and C_1 = 0.67 \pm 0.07 and D is the dimensionality of the system, i.e. for hard disk D=2.

\alpha = \frac{V-V_0}{V_0}

where V_0 is the close packed volume.


  1. B. J. Alder, W. G. Hoover, and D. A. Young "Studies in Molecular Dynamics. V. High-Density Equation of State and Entropy for Hard Disks and Spheres", Journal of Chemical Physics 49 pp. 3688-3696 (1968)