Event-chain Monte Carlo algorithms for hard-sphere systems.
TLDR
Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method, and reversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further.Abstract:
In this paper we present the event-chain algorithms, which are fast Markov-chain Monte Carlo methods for hard spheres and related systems. In a single move of these rejection-free methods, an arbitrarily long chain of particles is displaced, and long-range coherent motion can be induced. Numerical simulations show that event-chain algorithms clearly outperform the conventional Metropolis method. Irreversible versions of the algorithms, which violate detailed balance, improve the speed of the method even further. We also compare our method with a recent implementations of the molecular-dynamics algorithm.read more
Citations
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Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition
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Rejection-free Monte Carlo sampling for general potentials.
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References
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Equation of state calculations by fast computing machines
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
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Nonuniversal critical dynamics in Monte Carlo simulations
TL;DR: A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality, despite the fact that the algorithm violates dynamic universality at second-order phase transitions.
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Phase Transition for a Hard Sphere System
Berni J. Alder,T. E. Wainwright +1 more
TL;DR: In this article, a method for solving the simultaneous classical equation of motion of several hundred particles by means of fast electronic computers is described. But the method is not suitable for large numbers of particles.
Journal ArticleDOI
Collective Monte Carlo updating for spin systems.
TL;DR: A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality and its efficiency is demonstrated in the two-dimensional $\mathrm{O}(n)$ $\ensuremath{\sigma}$ models.
Journal ArticleDOI
Theory of Two-Dimensional Melting
TL;DR: In this article, the consequences of dislocation-mediated two-dimensional melting are worked out for triangular lattices, and the critical behavior, as well as the effect of a periodic substrate, is discussed.
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