Hard Discs on the Hyperbolic Plane

Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396, USA(Dated: February 1, 2008)We examine a simple hard disc fluid with no long range interactions on the two dimensional spaceof constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a naturalmechanism by which global crystalline order is frustrated, allowing us to construct a tractable modelof disordered monodisperse hard discs. We extend free area theory and the virial expansion to thisregime, deriving the equation of state for the system, and compare its predictions with simulationnear an isostatic packing in the curved space.