Hard disk model

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Hard disks are hard spheres in two dimensions. The hard disk intermolecular pair potential is given by[1] [2]

where is the intermolecular pair potential between two disks at a distance , and is the diameter of the disk. This page treats hard disks in a two-dimensional space, for three dimensions see the page hard disks in a three dimensional space.

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 ever since the early work of Alder and Wainwright [3]. In a recent publication by Mak [4] using over 4 million particles one appears to have the phase diagram isotropic , a hexatic phase, and a solid phase (the maximum possible packing fraction is given by [5]) . Similar results have been found using the BBGKY hierarchy [6] and by studying tessellations (the hexatic region: ) [7]. Experimental results [8].

Equations of state

Main article: Equations of state for hard disks

Virial coefficients

Main article: Hard sphere: virial coefficients

See also

References

Related reading

External links