Hard Discs on the Hyperbolic Plane
Statistical Mechanics
2007-12-03 v3 Soft Condensed Matter
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.
Cite
@article{arxiv.0708.4334,
title = {Hard Discs on the Hyperbolic Plane},
author = {Carl D. Modes and Randall D. Kamien},
journal= {arXiv preprint arXiv:0708.4334},
year = {2007}
}
Comments
4 pages, 3 figures, included, final version