The hexatic phase of the two-dimensional hard disk system

Abstract

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

Granular Thermodynamics

“…The intermediate phase is the same as that of equilibrium hard sphere/disk systems [5,6,7] showing the distinct signature of caging behavior (i.e., subdiffusive behavior at intermediate times, see Fig. 6, followed by diffusive behavior at long times) and is consistent with the hexatic phase in 2D equilibrium hard disks [8]. In the crystalline phase particles do not diffuse and sit in a system-filling hexagonal lattice for all times studied.…”

Melting of multilayer colloidal crystals confined between two walls

“…The intermediate hexatic phase was observed in many 2D systems including our NIPA monolayers [10], while the liquid-solid coexistence without a hexatic phase [43,44] and the hexaticliquid coexistence [45] were observed in other systems. In these coexistence states, or in the uniform hexatic phase, small defects are dispersed uniformly without condensing into large strips of liquid or lakes.…”

Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

“…For example, there are theoretical expectations that in simple liquids the first nucleating phase has the bcc structure [24−26]. Indeed this expectation is supported by atomistic simulations for the Lennard-Jones system [21,27] and by experiments showing metastable bcc nucleation in supersaturated superfluid 4 He, in preference to the stable hcp phase [28]. Atomistic models based on the density functional technique (DFT) suggest that crystallization might happen via a dense liquid/amorphous precursor phase [29,30] reminiscent to the two-step transition seen in 2d colloidal systems [16−18].…”