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

Abstract

We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.

Hard-sphere melting and crystallization with event-chain Monte Carlo

“…The collision force b ij = r ij · v ij is defined between the relative positions and the relative velocities of the collision partners 11,17 . In ECMC, the pressure P * can be evaluated from the mean excess chain displacement 13 :…”

“…A rejection-free hard-sphere "event-chain" Monte Carlo algorithm (ECMC) 9 has recently allowed to speed up equilibration for two-dimensional hard disks by roughly two orders of magnitude compared to the eventdriven molecular dynamics 5,10 (EDMD) and to local Monte Carlo 11,12 (LMC). In ECMC, a randomly sampled starting sphere moves along a straight line until the latter collides with another sphere, which then moves in the same direction until it collides itself with yet another sphere.…”

Effect of a potential softness on the solid-liquid transition in a two-dimensional core-softened potential system

“…The "toy" model for the investigation of the melting transition in 2D, hard-disk system, have been studied in a large number of computer simulations without unambiguous conclusion about the melting scenario [53][54][55][56]61]. It was even suggested an unexpected possibility of the firstorder hexatic-isotropic liquid transition [59,60].…”

Clustering impact regime with shocks in freely evolving granular gas

“…At microscopic molecular dynamics level, the IHS model can completely be characterized by three independent parameters: the total number of disks N, the packing fraction ν, and the restitution coefficient r. In case of r = 1, the system is govern by only solid-fluid phase transition, so-called "Alder transition" (See, recent progress in Refs. [15,16]). The whole systems with a side length L in the two dimensional (2D) square systems include monodisperse hard disks up to N = 4096 2 with a radius of disk σ, in which we adopted the periodic boundary conditions.…”