Two-step melting in two dimensions: First-order liquid-hexatic transition

TL;DR

This paper demonstrates that in two-dimensional hard-disk systems, melting occurs via a two-step process involving a first-order liquid-hexatic transition followed by a continuous hexatic-solid transition, resolving a long-standing debate.

Contribution

It provides the first direct evidence that the liquid-hexatic transition in 2D hard disks is first-order, while the hexatic-solid transition is continuous, clarifying the melting mechanism.

Findings

Liquid-hexatic transition is first-order.

Hexatic-solid transition is continuous.

Melting proceeds via a two-step process.

Abstract

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed on after fifty years of studies. A recent Monte Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first-order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational and experimental research.