Rejection-free Monte Carlo sampling for general potentials

Abstract

A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is event-driven; i.e., at scheduled times the collisions occur. A unique feature of the new method is that smooth potentials (instead of only step-wise changing ones) can be used. In addition to an event-driven approach, where all particles move simultaneously, we introduce a straight event-chain implementation. As proof of principle, a system of Lennard-Jones particles is simulated.

Collective translational and rotational Monte Carlo moves for attractive particles

“…First, event-chain Monte Carlo [34,35] displaces chains of particles in an efficient way. Second, event-driven Monte Carlo [36] displaces single particles, but selects and accepts them in a way which is dynamic. It would be interesting to see how these algorithms complement the VMMC methods in capturing the kinetic and thermodynamic crossover in glassy systems [26,37].…”

“…In contrast to Sec. V, the difference between the realizations can not be ignored, and needs to be corrected with a bias in the acceptance probability (36). The bias is derived in Appendix B and the corresponding early rejection scheme validated in Appendix C 3.…”

Event-chain Monte Carlo for classical continuous spin models

“…In the present work, we show that the novel eventchain Monte Carlo (ECMC) paradigm [14][15][16], that has already been very successful in particle systems [17][18][19][20], can also be applied to the XY model and the XY spin glass model. The paradigm breaks all three principles of the conventional Markov-chain scheme: Moves are infinitesimal rather than finite, although an event-driven scheme allows to recover finite displacements [16].…”

“…The paradigm breaks all three principles of the conventional Markov-chain scheme: Moves are infinitesimal rather than finite, although an event-driven scheme allows to recover finite displacements [16]. In onedimensional systems, the moves do not change with time.…”

“…In an eventdriven approach [15,16], the algorithmic complexity can be made to scale with the number of liftings: The lifting variable being set to k , the angle φ k now rotates clockwise until the "event", i.e. a lifting move, is produced through a rejection by a neighbor l. The lifting variable is updated to l , φ l rotates clockwise, etc.…”