Source-linked AI summary
Event-chain Monte Carlo algorithms for hard-sphere systems
Etienne P. Bernard, Werner Krauth, David B. Wilson
TL;DR
Hard-sphere Monte Carlo methods had changed little, especially at high densities. The paper introduces rejection-free event-chain algorithms that move particle chains, including irreversible variants, and finds they outperform traditional Metropolis methods while achieving high collision-processing rates.
Problem
Monte Carlo algorithms for hard spheres had changed little since the 1950s, especially for high densities.
Method
The paper introduces rejection-free event-chain Monte Carlo algorithms that displace arbitrarily long chains of spheres, including irreversible versions that violate detailed balance while preserving the correct stationary distribution.
Results
Event-chain algorithms clearly outperform traditional Metropolis methods; the xy SEC implementation processes about 3 × 10^10 collisions per hour, roughly 5 times faster than the compared molecular-dynamics implementation.
Takeaways & Limitations
Coherent long-chain motion and irreversible dynamics can accelerate equilibration and improve performance for dense hard-disk and hard-sphere simulations.
Takeaways & Limitations
CPU times for convergence remain extremely large, and full convergence of systems with 10^6 particles at high densities remains barely within reach.
Abstract
from arXiv · showhide
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.