Hard-disk equation of state: first-order liquid-hexatic transition in two dimensions with three simulation methods

Area of Science:

• Physics
• Computational Physics
• Materials Science

Background:

• The hard-disk system is a fundamental model in statistical mechanics.
• Understanding phase transitions, like melting, is crucial for materials science.
• Previous studies established the equation of state for hard disks.

Purpose of the Study:

• To perform large-scale computer simulations of the hard-disk system near its melting transition.
• To compare the performance of different simulation methods (local Monte Carlo and event-driven molecular dynamics) in sampling configuration space.
• To confirm the nature of the melting transition and identify coexisting phases.

Main Methods:

• Large-scale computer simulations using a massively parallel implementation of the local Monte Carlo method.
• Event-driven molecular dynamics simulations.
• Analysis of the equation of state.
• Visualization of phase coexistence using the orientational order parameter field.
• Analysis of positional order.

Main Results:

• The simulations successfully reproduced the known equation of state for hard disks.
• Both local Monte Carlo and event-driven molecular dynamics methods were analyzed for their efficiency in sampling configuration space.
• The first-order nature of the melting phase transition in hard disks was confirmed.
• Visualizations clearly showed phase coexistence.
• Analysis of positional order provided evidence for the existence of the hexatic phase.

Conclusions:

• The study validates the accuracy of the simulated equation of state for hard disks.
• The findings confirm the first-order nature of the melting transition in this system.
• The existence of the hexatic phase is supported by the analysis of positional order.