Parallelized event chain algorithm for dense hard sphere and polymer systems

TL;DR

This paper introduces a parallelized event chain Monte Carlo algorithm for dense hard sphere and polymer systems, improving computational efficiency while maintaining correctness through careful balance considerations.

Contribution

It presents a novel parallelization approach for the event chain algorithm, including a detailed balance-preserving method and analysis of optimal parallelization levels.

Findings

Parallelization significantly speeds up simulations.

Correctness depends on detailed balance at the sweep level.

Optimal parallelization degree is identified.

Abstract

We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.