Editing Liu hard disk equation of state
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The '''Liu''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by Eq. 1, 9 and 13 of | The '''Liu''' [[Equations of state | equation of state]] for [[hard disks]] (2-dimensional [[hard sphere model | hard spheres]]) is given by Eq. 1, 9 and 13 of | ||
<ref>[https://arxiv.org/abs/2010.10624 | <ref>[https://arxiv.org/abs/2010.10624]</ref>. | ||
For the stable fluid: | For the stable fluid: | ||
:<math>Z_v = \frac{1 + \eta^2/8 + \eta^ | :<math>Z_v = \frac{1 + \eta^2/8 + \eta^4/18 - 4 \eta^4/21}{(1-\eta)^2} </math> | ||
where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where | where the packing fraction is given by <math>\eta = \pi \rho \sigma^2 /4 </math> where <math>\sigma</math> is the diameter of the disks. | ||
The EoS for the stable fluid, liquid-hexatic transition region and hexatic: | The EoS for the stable fluid, liquid-hexatic transition region and hexatic: | ||
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<math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math> | <math>Z_{solid} = \frac{2}{\alpha} + 1.9 + \alpha - 5.2 \alpha^2 + 114.48 \alpha^4</math> | ||
and <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2} | and <math>\alpha = \frac{2}{3^{1/2} \rho \sigma^2}</math> | ||
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| <math>m_2</math> || 56 | | <math>m_2</math> || 56 | ||
|- | |- | ||
| <math> | | <math>c </math> || 0.75 | ||
|} | |} | ||