2013/01/21 by Sebastian C. Kapfer, Werner Krauth
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.soft #physics.comp-ph
paper · pdf · doi:10.1088/1742-6596/454/1/012031
published as Journal of Physics: Conference Series, Volume 454, Issue 1, article id. 012031 (2013)
arxiv created 2013/01/21 · arxiv updated 2014/02/10
The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound influence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were first discussed for this model. Here we reformulate hard-disk Monte Carlo algorithms in terms of another classic problem, namely the sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in 1953, appears as a sequence of random walks in high-dimensional polytopes, while the moves of the more powerful event-chain algorithm correspond to molecular dynamics evolution. We determine the convergence properties of Monte Carlo methods in a special invariant polytope associated with hard-disk configurations, and the implications for convergence of hard-disk sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present results for a multicore implementation.