First-order liquid-hexatic phase transition in hard disks
msra(2011)
摘要
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.
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关键词
molecular dynamic,statistical physics,numerical simulation,monte carlo algorithm,first order,phase transition,phase separation,three dimensions,statistical mechanics
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