Melting of systems of hard disks by Monte Carlo simulations

Fernández, Julio F.; Alonso, Juan J.; Stankiewicz, Jolanta

doi:10.1103/physreve.55.750

Cited by 29 publications

(22 citation statements)

References 49 publications

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“…First-order melting has been reported in the literature, 19,[21][22][23] while other calculations support a continuous transition. 24,25 The critical properties of the KTHNY transition are a consequence of the renormalization effect that small-scale fluctuations have on large-scale fluctuations. For this mechanism to be operative, well-separated length scales must exist, suggesting a minimum size for numerical simulations in two dimensions of 10 4 .…”

Section: Introductionmentioning

confidence: 99%

Characterization of the melting transition in two dimensions at vanishing external pressure using molecular dynamics simulations

et al. 2011

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A molecular dynamics study of a two-dimensional system of particles interacting through a Lennard-Jones pairwise potential is performed at a fixed temperature and vanishing external pressure. As the temperature is increased, a solid-to-liquid transition occurs. When the melting temperature T c is approached from below, there is a proliferation of dislocation pairs and the elastic constant approaches the value predicted by the KTHNY theory. In addition, as T c is approached from above, the relaxation time increases, consistent with an approach to criticality. However, simulations fail to produce a stable hexatic phase using systems with up to 90,000 particles. A significant jump in enthalpy at T c is observed, consistent with either a first order or a continuous transition. The role of external pressure is discussed.

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Section: Introductionmentioning

confidence: 99%

Characterization of the melting transition in two dimensions at vanishing external pressure using molecular dynamics simulations

et al. 2011

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“…The observed phase is not within a possible first-order phase transition since the pressure 8.04(1) at ρ = 0.918 is higher than that of such a transition 7.95(1) [19]. Therefore, a one-stage continuous transition [23,24] as well as a first-order phase transition from the isotropic to the solid phase can be ruled out. Taking the results of previous measurements [18,19] a KTHNY-like phase transition is most likely.…”

mentioning

confidence: 98%

“…They also favoured a first-order phase transition. In contrast to this, Fernández, Alonso and Stankiewicz [23,24] 1 predicted a one-stage continuous melting transition, i.e. a scenario with a single continuous transition and consequently without a hexatic phase.…”

mentioning

confidence: 99%

“…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%

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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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“…While some studies support the KTHNY scenario [16,[26][27][28][29][30][31][32], a comparable number conclude that the transition is first order [15,[33][34][35][36]. In fact, contradictory conclusions have been reached even for the same interaction potential, so that there is no consensus regarding the character of the transition.…”

Section: Melting By Proliferation Of Topological Defectsmentioning

confidence: 85%

Melting transition of a network model in two dimensions

Gompper

Kroll

2000

Eur. Phys. J. E

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The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths.PACS. 61.20.Ja Computer simulation of liquid structure -61.72.Bb Theories and models of crystal defects -64.70.Dv Solid-liquid transitions

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Melting of systems of hard disks by Monte Carlo simulations

Cited by 29 publications

References 49 publications

Characterization of the melting transition in two dimensions at vanishing external pressure using molecular dynamics simulations

Characterization of the melting transition in two dimensions at vanishing external pressure using molecular dynamics simulations

The hexatic phase of the two-dimensional hard disk system

Melting transition of a network model in two dimensions

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