Hard disks

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Hard disks are hard spheres in two dimensions. The hard disk intermolecular pair potential is given by

$\Phi_{12}\left( r \right) = \left\{ \begin{array}{lll} \infty & ; & r < \sigma \\ 0 & ; & r \ge \sigma \end{array} \right.$

where $\Phi_{12}\left(r \right)$ is the intermolecular pair potential between two disks at a distance $r := |\mathbf{r}_1 - \mathbf{r}_2|$ , and $σ$ is the diameter of the disk.

[edit] Phase transitions

Despite the apparent simplicity of this model/system, the phase behaviour and the nature of the phase transitions remains an area of active study. In a recent publication by Mak (Ref. 5) using over 4 million particles $(2048 2)$ one appears to have the phase diagram isotropic $(\rho \leq 0.890)$ hexatic $(ρ > 0.920)$ solid.