Event-chain Monte Carlo algorithms for three- and many-particle interactions

TL;DR

This paper extends event-chain Monte Carlo algorithms to efficiently handle systems with three- or many-particle interactions, broadening their applicability in statistical physics simulations.

Contribution

The authors develop a generalized framework for event-chain Monte Carlo algorithms that accommodates arbitrary many-particle interactions, ensuring maximal global balance.

Findings

Validated the generalized algorithms on three different systems

Demonstrated improved applicability over traditional pairwise interaction methods

Confirmed the algorithms' efficiency through comparison with local Monte Carlo simulations

Abstract

We generalize the rejection-free event-chain Monte Carlo algorithm from many particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between particles and obtain a general set of equations for lifting probabilities, the solution of which guarantees maximal global balance. We validate the resulting three-particle event-chain Monte Carlo algorithms on three different systems by comparison with conventional local Monte Carlo simulations: (i) a test system of three particles with a three-particle interaction that depends on the enclosed triangle area; (ii) a hard-needle system in two dimensions, where needle interactions constitute three-particle interactions of the needle end points; (iii) a semiflexible polymer chain with a bending energy, which constitutes a three-particle interaction of neighboring chain beads. The examples demonstrate that the generalization to many-particle interactions broadens the applicability of event-chain algorithms considerably.