Extended defects in hard disk system and melting criteria

TL;DR

This paper investigates melting in the hard disk system using defect accumulation and jamming, establishing bounds on volume ratios at melting and confirming the transition to anisotropic liquid as predicted by BKT theory.

Contribution

It introduces analytical melting criteria for the hard disk system based on defect accumulation and jamming, with bounds on volume ratios at transition points.

Findings

Melting occurs within volume ratio bounds 25/21 and 5/4.

2D crystal melts into an anisotropic liquid, consistent with BKT theory.

Transition from anisotropic to isotropic liquid occurs between volume ratios 5/4 and 13/9.

Abstract

The hard sphere model is widely used in description of fluids and solid media as a zero approximation to real systems. Despite the uniqueness of the model, few analytical results are known for it, both for the 2D and 3D cases. In present research we have investigated melting of the hard disk system by considering accumulation of extended defects of a certain type in the crystaline phase, and jamming of the disk packing. It results in formulation of melting criteria with lower and upper bounds on volume ratio at melting transition: $25/21 \le V/V_0 \le 5/4$. It was found that, in full agreement with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory, the 2D crystal melts into anisotropic liquid. The second transition, which is the transition between anisotropic and isotropic liquid has volume ratio $5/4 \le V/V_0 \le 13/9$.