Hard Disks on the Hyperbolic Plane

2007/08/31 by Carl D. Modes, Randall D. Kamien · 6 citations
Engineering · Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Phase Equilibria and Thermodynamics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.99.235701

published as Phys. Rev. Lett. 99 (2007) 235701 · 4 pages, 3 figures, included, final version

arxiv created 2007/11/30 · openalex publication_date 2007/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine a simple hard disk 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 disks. 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.

Citations

• Jamming at zero temperature and zero applied stress: The epitome of disorder

Cited by

• Curvature-induced frustration in theXYmodel on hyperbolic surfaces
• Percolation on hyperbolic lattices
• Counterintuitive ground states in soft-core models
• Geometrical frustration in two dimensions: Idealizations and realizations of a hard-disk fluid in negative curvature
• Fluid-bicontinuous gels stabilized by interfacial colloids: low and high molecular weight fluids
• Spherical foams in flat space