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

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.

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• Event-Chain Monte-Carlo Simulations of Dense Soft Matter Systems
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• Irreversible Markov chains in spin models: Topological excitations
• Mixing and perfect sampling in one-dimensional particle systems
• Multithreaded event-chain Monte Carlo with local times
• Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals
• PDMP characterisation of event-chain Monte Carlo algorithms for particle systems
• A general perspective on the Metropolis-Hastings kernel
• Non-reversible Monte Carlo: an example of 'true' self-repelling motion
• Large-scale dynamics of event-chain Monte Carlo
• Molecular simulation from modern statistics: Continuous-time, continuous-space, exact
• Control of probability flow in Markov chain Monte Carlo -- Nonreversibility and lifting
• The Coordinate Sampler: A Non-Reversible Gibbs-like MCMC Sampler
• Markov-chain sampling for long-range systems without evaluating the energy
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality
• Bosonized one-dimensional quantum systems through enhanced event-chain Monte Carlo
• Necessary and sufficient symmetries in Event-Chain Monte Carlo with generalized flows and Application to hard dimers
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs
• Accelerating Multicanonical Sampling with Irreversibility
• Kinetic Event-Chain Algorithm for Active Matter