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.
Published Version
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