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

Area of Science:

• Computational Physics
• Materials Science
• Statistical Mechanics

Background:

• Simulating phase transitions like crystallization and melting is crucial for understanding materials.
• Traditional methods like local Monte Carlo (LMC) can be computationally intensive for large systems.

Purpose of the Study:

• To compare the efficiency of local Monte Carlo (LMC), event-chain Monte Carlo (ECMC), and event-driven molecular dynamics (EDMD) for simulating hard-sphere systems.
• To investigate nucleation dynamics in the NVE ensemble using these algorithms.

Main Methods:

• Simulations of up to one million three-dimensional hard spheres.
• Implementation and comparison of LMC, ECMC, and EDMD algorithms.
• Study of nucleation from crystal to liquid and liquid to crystal phases in the NVE ensemble.

Main Results:

• All three algorithms (LMC, ECMC, EDMD) demonstrate rigorous agreement in equilibrium properties.
• ECMC and EDMD achieve equilibrium orders of magnitude faster than LMC.
• ECMC significantly outperforms EDMD, especially in achieving crystal equilibration from disordered states at high densities.

Conclusions:

• ECMC offers a substantial speedup over LMC and EDMD for hard-sphere simulations.
• ECMC's ease of implementation for various potentials suggests broad applicability.
• Potential applications include studying jamming, glass physics, and other disordered systems.