Bernard Krauth 2011

From Werner KRAUTH

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E. P. Bernard, W. Krauth Two-step melting in two dimensions: First-order liquid-hexatic transition (Physical Review Letters 107, 155704 (2011))

Abstract: The hard-disk model has exerted outstanding influence on computational physics and statistical mechanics. Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods and by molecular dynamics. It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur even though such systems cannot develop long-range crystalline order. Scores of theoretical, computational, and experimental works have analysed this fundamental melting transition, without being able to settle its nature. The first-order melting scenario between a liquid and a solid (as in three dimensions), and the Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY) scenario with an intermediate hexatic phase separated by continuous transitions from the liquid and the solid have been mainly focussed upon. Here we show by large-scale simulations using the powerful Event-chain Monte Carlo algorithm that the hard-disk system indeed possesses a narrow hexatic phase, where orientational order is maintained across large samples while positional order is short-ranged. However, in difference with the KTHNY scenario, the liquid-hexatic phase transition is proven to be first-order. In simulations at fixed volume and number of disks, we identify a two-phase region, where the liquid with large but finite orientational correlation length coexists with the hexatic. At higher densities, we reach the pure hexatic phase, and then witness the transition into the solid phase characterised by quasi-long range positional order. Our work closes a crucial gap in the understanding of one of the fundamental models in statistical physics, which is at the basis of a large body of theoretical and experimental work in films, suspensions, and other condensed-matter systems.

Electronic version (from arXiv, final version, to appear in PRL)

Electronic version (from arXiv, original version)

Illustration

Here are pictures of the local orientations (upper panels) and the local densities (lower panels) for the 1024x1024 systems at various densities. Phase separation is easily visible.
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