Hard Discs on the Hyperbolic Plane

Abstract

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.

4 pages, 3 figures, included, final version

References in corpus (3)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Why is Random Close Packing Reproducible?
• Periodic boundary conditions on the pseudosphere

Cited by in corpus (4)

• Tuning the fragility of a glassforming liquid by curving space
• Fluid-bicontinuous gels stabilized by interfacial colloids: low and high molecular weight fluids
• Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature
• Simple equation of state for hard disks on the hyperbolic plane