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

Abstract

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