On the equation of state of the hard disk system: the fluid-hexatic phase transition

Abstract

The accuracy of four approximations proposed along time as equations of state for a homogeneous system of hard disks is compared against molecular dynamics results of 10 5 disks in equilibrium [L. Mier-y-Terán, J. Munguía and J. Antonio Moreno-Razo, Mol. Phys. (2023). doi:10.1080/00268976.2023.2288702]. Three of the equations studied here are Padé approximants. Only one of the approximations studied, based on the virial expansion of the compressibility factor of the homogeneous fluid, is considered to have sound physical grounds. Assuming that the total pressure predicted generates the positional part of the Helmholtz free energy, only, the four approximations, combined with the molecular dynamics simulation results referred above, allow identifying four linear regions, where different orientational processes can be associated with the well known steps of the melting transition. Results for a finite system are consistent with the KTHNY theory. In particular, under this assumption, the four approximations, with small quantitative differences, show the ordering effects present in the fluid at the low-density-end of the fluid-hexatic first-order phase transition. It is shown that the latter region continues to exist under the assumption proposed. In addition, a linear combination of the virial and compressibility coefficients is used to obtain a more accurate version of the Carnahan-Starling type approximation for the hard-disk system.