Large-scale dynamics of event-chain Monte Carlo

Event-chain Monte Carlo (ECMC) accelerates the sampling of hard-sphere systems, and has been generalized to the potentials used in classical molecular simulations. Rather than imposing detailed balance on the transition probabilities, the method enforces a weaker global-balance condition in order to guarantee convergence to equilibrium. In this paper, we generalize the factor-field variant of ECMC to higher space dimensions. In the two-dimensional fluid phase, factor-field ECMC saturates the lower bound z = 0 for the dynamical scaling exponent for local dynamics, whereas molecular dynamics is characterized by z = 1 and local Metropolis Monte Carlo by z = 2. In the presence of hexatic order, factor fields are not found to speed up the convergence. We note that generalizations of factor fields could couple to orientational order.