Hard-sphere melting and crystallization with event-chain Monte Carlo
Masaharu Isobe,Werner Krauth +1 more
TL;DR: ECMC can be trivially implemented for hard-sphere and for soft-spheres potentials, and it is suggested possible applications of this algorithm for studying jamming and the physics of glasses, as well as disordered systems.
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Abstract: We simulate crystallization and melting with local Monte Carlo (LMC), with 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.
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References
Sampling from a polytope and hard-disk Monte Carlo
Sebastian C. Kapfer,Werner Krauth +1 more
- 12 Aug 2013
TL;DR: In this article, the authors reformulate hard disk Monte Carlo algorithms in terms of another classic problem, namely the sampling from a polytope, and determine the convergence properties of Monte Carlo methods in a special invariant polytopope associated with hard disk configurations, and the implications for convergence of hard disk sampling.
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Crystallization: Colloidal suspense
TL;DR: In this article, it was shown that, from an amorphous precursor, crystallites with different structures can develop, from a small nucleus that already bears the symmetry of its end phase.
Entropy difference between crystal phases
TL;DR: In a recent paper as mentioned in this paper, Woodcock reported the results of a molecular dynamics study in which he claimed to have finally determined the free-energy difference between the hexagonal close-packed (h.c.p.) and face-centred cubic (f.c.) phases of a crystal of (classical) hard spheres.
Interfacial Tension Effects in Finite, Periodic, Two‐Dimensional Systems
Joseph E. Mayer,Wm. W. Wood +1 more
TL;DR: In this article, the authors consider a two-dimensional system whose pressure specific area (p-v) isotherm displays a first-order phase transition in the thermodynamic limit, i.e., as the number of molecules N and the total area V both tend to infinity for various fixed specific volumes v=V/N.
Two-dimensional melting: from liquid-hexatic coexistence to continuous transitions.
TL;DR: The phase diagram of two-dimensional continuous particle systems is studied using the event-chain Monte Carlo algorithm and it is demonstrated that Yukawa particles likewise may follow either the KTHNY or the hard-disk melting scenario, depending on the Debye-Hückel screening length as well as on the temperature.