Hard sphere simulation in statistical physics — methodologies and applications

Abstract

The hard disk/sphere systems are one of the most important models to investigate fundamental problems in the field of statistical physics. From the numerical point of view, simulation results on the melting/crystallisation of this model were one of the historical milestones. After pioneering works on this issue by Monte Carlo (MC) and molecular dynamics (MD) methods in 1957, enormous implementations of algorithms and a wide variety of applications including general potentials have been investigated. Here, we revisit the hard disk/sphere systems with modern algorithms, especially for event-chain MC and event-driven MD, where we propose the ‘Hybrid Scheme’, namely, event-chain MC for equilibration and event-driven MD for calculation of dynamical properties. This paper addresses (i) short review of novel methodologies and physical properties in the hard disk/sphere systems and (ii) recent applications of those methods in the two- and three-dimensional melting/crystallisation including the binary mixture systems. We expect further promising applications in the non-equilibrium systems such as transport phenomena (long-time tail and molasses tail) and dissipative (granular) systems.

Keywords:

• Hard sphere
• event-driven molecular dynamics
• event-chain Monte Carlo

Acknowledgements

The author is grateful to Profs B.J. Alder, W. Krauth and D. Chandler for or stimulating and fruitful discussions on this topics. He also grateful to Dr K. Niki for helpful comments for improving the manuscript.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This study was supported by JSPS Grant-in-Aid for Scientific Research No. [26400389]. Part of the computations were performed using the facilities of the Supercomputer Center, ISSP, University of Tokyo.