Choosing the right event (in non-reversible event-chain Monte Carlo)

The general framework of event-chain Monte Carlo (ECMC) constructs non-reversible Markov chains for continuous statistical-physics models ranging from hard-disk systems to long-range interacting molecular systems. Over recent years, several algorithms from the family of ECMC have been proposed, which, in the event-driven formulation of ECMC, only differ in their treatment of events (that is, e.g., of disk collisions in a hard-disk system). Still, we show that different variants can have widely different performances. As a first example, we consider locally stable sparse hard-disk packings [1]. Using a scaling theory confirmed by simulation results, we obtain two classes for the escape from slightly relaxed hard-disk packings parameterized by a relaxation parameter. In one class, the escape time varies algebraically with the relaxation parameter. In the other class, the escape time only scales as the logarithm of the relaxation parameter. As a second example, we consider integrated autocorrelation times in dense systems of flexible extended hard-disk dipoles [2]. Here, the ECMC variants show order-of-magnitude spreads. We expect the performance differences to carry over to long-range interacting molecular systems, where the choice of the optimal ECMC variant is thus highly important.