Virial equation-of-state for the hard-disk fluid

TL;DR

This paper derives an accurate, closed-form equation-of-state for the two-dimensional hard-disk fluid using virial coefficients, showing convergence up to close packing and deviations near the ordering transition.

Contribution

It introduces a virial-based equation-of-state for 2D hard disks that parallels recent 3D hard sphere results and analyzes its convergence properties.

Findings

The virial series converges up to close packing density.

The equation-of-state accurately describes the fluid's behavior.

Deviations occur near the ordering transition.

Abstract

Virial coefficients for the two-dimensional hard-disk fluid, when expressed in powers of density relative to maximum close packing, lead to an accurate closed equation-of-state for the equilibrium fluid, analogous to that recently found for hard spheres. The 2D series also converges for all densities up to a negative pole at close packing density. The virial pressure begins to deviate from the thermodynamic fluid in the approach to the ordering transition.