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

TL;DR

This study compares local Monte Carlo, event-chain Monte Carlo, and event-driven molecular dynamics in simulating melting and crystallization of up to one million hard spheres, highlighting ECMC's superior efficiency and potential applications.

Contribution

The paper demonstrates that ECMC, LMC, and EDMD yield consistent equilibrium results and shows ECMC's faster convergence, especially in high-density crystallization scenarios.

Findings

ECMC approaches equilibrium faster than LMC and EDMD.

ECMC is particularly efficient for high-density crystal formation.

Implementations of the three algorithms produce consistent equilibrium properties.

Abstract

We simulate crystallization and melting with local Monte Carlo (LMC), event-chain Monte Carlo (ECMC), and with event-driven molecular dynamics (EDMD) in systems with up to one million three-dimensional hard spheres. We illustrate that our implementations of the three algorithms rigorously coincide in their equilibrium properties. We then study nucleation in the NVE ensemble from the fcc crystal into the homogeneous liquid phase and from the liquid into the homogeneous crystal. ECMC and EDMD both approach equilibrium orders of magnitude faster than LMC. ECMC is also notably faster than EDMD, especially for the equilibration into a crystal from a disordered initial condition at high density. ECMC can be trivially implemented for hard-sphere and for soft-sphere potentials, and we suggest possible applications of this algorithm for studying jamming and the physics of glasses, as well as disordered systems.