Analysis of the ordering transition of hard disks through the Mayer cluster expansion

TL;DR

This paper uses a matrix representation of virial coefficients to accurately describe the fluid phase of 2D hard disks up to the phase transition, supporting a second order transition into a Hexatic phase.

Contribution

It introduces a matrix approach to virial coefficients for 2D hard disks, providing detailed insights into the phase transition and critical behavior.

Findings

Fluid phase terminates at the transition point

Transition supports a second order phase transition into Hexatic phase

Calculated transition density and pressure agree with Monte-Carlo results

Abstract

The available virial coefficients for the 2D hard disks model are transformed into a matrix representation of the thermodynamic potentials, which allows for an accurate description of the whole fluid phase, up to the phase transition. We find that the fluid phase terminates at the transition point, supporting the Kosterlitz-Thouless-Halperin-Nelson-Young picture of a second order phase transition into a Hexatic phase. The density and pressure at the transition are calculated from the available first ten virial coefficients, and are found to be in excellent agreement with recent Monte-Carlo calculations. Finally, we calculate the equation of state in the critical region.