Hard Discs on the Hyperbolic Plane

Details Hard Discs on the Hyperbolic Plane Hard Discs on the Hyperbolic Plane

2007-08-31

arxiv.org/abs/0708.4334v3

Phys. Rev. Lett. 99 (2007) 235701

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, included, final version

Scientific paper

10.1103/PhysRevLett.99.235701

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard discs. We extend free area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.

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