First-order melting transition of the hard-disk system

Lee, Jooyoung; Strandburg, Katherine J.

doi:10.1103/physrevb.46.11190

Cited by 106 publications

(87 citation statements)

References 27 publications

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“…Recently the layered close-packed crystalline structure and their structural transition were observed in experiments with dust rf discharge [3] and with ion layered crystals in ion traps [4]. Motivated by the theoretical works of Nelson, Halperin [5], and Young [6] who developed a theory for a two stage continuous melting of a two dimensional (2D) crystal and which was based on ideas of Berenzinskii [7], Kosterlitz and Thouless [8], several experimental [9][10][11][12] and theoretical studies [13][14][15][16][17][18][19][20][21][22][23][24][25] were devoted to the melting transition of mainly single layer crystals. In this case the hexagonal lattice is the most energetically favored structure for potentials of the form 1/r n [26,27].…”

Section: Introductionmentioning

confidence: 99%

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Schweigert

Peeters

1999

Phys. Rev. B

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The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the MonteCarlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard-Jones and 1/r 12 repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.

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Section: Introductionmentioning

confidence: 99%

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Schweigert

Peeters

1999

Phys. Rev. B

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“…The hexatic phase is characterized by exponential positional but quasi-long range orientational correlations. It has long been discussed whether the melting transition follows a one-step first-order scenario between the liquid and the solid (without the hexatic) as in three spatial dimensions [6]), or whether it agrees with the celebrated Kosterlitz, Thouless [7], Halperin, Nelson [8] and Young [9] (KTHNY) two-step scenario with a hexatic phase separated by continuous transitions from the liquid and the solid [10][11][12][13][14][15][16][17][18]. Two-dimensional melting was discovered [4] in the simplest particle system, the hard-disk model.…”

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Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition

2011

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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. Generic two-dimensional particle systems cannot crystallize at finite temperature [1][2][3] because of the importance of fluctuations, yet they may form solids [4]. This paradox has provided the motivation for elucidating the fundamental melting transition in two spatial dimensions. A crystal is characterized by particle positions which fluctuate about the sites of an infinite regular lattice. It has long-range positional order. Bond orientations are also the same throughout the lattice. A crystal thus possesses long-range orientational order. The positional correlations of a two-dimensional solid decay to zero as a power law at large distances. Because of the absence of a scale, one speaks of "quasi-long range" order. In a two-dimensional solid, the lattice distortions preserve long-range orientational order [5], while in a liquid, both the positional and the orientational correlations decay exponentially.Besides the solid and the liquid, a third phase, called "hexatic", has been discussed but never clearly identified in particle systems. The hexatic phase is characterized by exponential positional but quasi-long range orientational correlations. It has long been discussed whether the melting transition follows a one-step first-order scenario between the liquid and the solid (without the hexatic) as in three spatial dimensions Two-dimensional melting was discovered [4] in the simplest particle system, the hard-disk model. Hard disks (of radius σ) are structureless and all configurations of nonoverlapping disks have zero potential energy. Two isolated disks only feel the hard-core repulsion, but the other disks mediate an entropic "depletion" interaction (see, e.g., [19]). Phase transitions result from an "order from disorder" phenomenon: At high density, ordered configurations can allow for larger local fluctuations, thus higher entropy, than the disordered liquid. For hard disks, no difference exists between the liquid and the gas. At fixed density η, the phase diagram is independent of temperature T = 1/k B β, and the pressure is proportional to T , as discovered by D. Bernoulli in 1738. Even for this basic model, the nature of the melting transition has not been agreed on.The hard-disk model has been simulated with the...

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“…But the results of such small systems are affected by large finite-size effects. Simulations performed in the last years used Monte Carlo (MC) techniques either with constant volume (NV T ensemble) [11,12,13,14,15,16,17,18,19,20,21] or constant pressure (NpT ensemble) [22,23,24]. Zollweg, Chester and Leung [11] made detailed investigations of large systems up to 16384 particles, but draw no conclusives about the order of the phase transition.…”

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confidence: 99%

“…The analysis of Zollweg and Chester [12] for the pressure gave an upper limit for a first-order phase transition, but is compatible with all other scenarios. Lee and Strandburg [22] used isobaric MC simulations and found a double-peaked structure in the volume distribution. Lee-Kosterlitz scaling led them to conclude that the phase transition is of first-order.…”

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confidence: 99%

The hexatic phase of the two-dimensional hard disk system

Jaster¹

2004

Physics Letters A

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We report Monte Carlo results for the two-dimensional hard disk system in the transition region. Simulations were performed in the N V T ensemble with up to 1024 2 disks. The scaling behaviour of the positional and bond-orientational order parameter as well as the positional correlation length prove the existence of a hexatic phase as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.The analysis of the pressure shows that this phase is outside a possible first-order transition.Key words: Hard disk model, Two-dimensional melting, KTHNY theory PACS: 64.70.Dv, 64.60.CnThe nature of the two-dimensional melting transition has been an unsolved problem for many years [1,2]. The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [3,4,5,6] predicts two continuous transitions. The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation unbinding transition to the hexatic phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination unbinding transition which transforms this hexatic phase into an isotropic phase (short-range positional and orientational order). An alternative scenario has been proposed by Chui [7,8]. He presented a theory via spontaneous generation of grain boundaries, i.e. collective excitations of dislocations. He found that grain boundaries may be generated before the dislocations unbind if the core energy of dislocations is sufficiently small, and predicted a first-order transition. This is characterized by a coexistence region of the solid and isotropic phase, while no hexatic phase exists. Another proposal was given by Glaser and Clark [2]. They considered a detailed theory where the transition is handled as a condensation of localized, thermally generated geometrical defects and found also a first-order transition. Calculations based on the density-functional approach were done by Ryzhov and

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First-order melting transition of the hard-disk system

Cited by 106 publications

References 27 publications

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition

The hexatic phase of the two-dimensional hard disk system

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