Event-chain Monte Carlo with factor fields

Abstract

We study the dynamics of one-dimensional (1D) interacting particles simulated with the eventchain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular-dynamics. We show, using numerical simulations, that they grow only with the square root of the systems size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.arXiv:1812.02494v1 [cond-mat.stat-mech]

JeLLyFysh-Version1.0 — a Python application for all-atom event-chain Monte Carlo

“…Event-chain Monte Carlo (ECMC) is an irreversible continuous-time Markovchain algorithm [5,28] that often equilibrates faster than its reversible counterparts [30,19,22,23,24]. ECMC has been successfully applied to the classic Nbody all-atom problem in statistical physics [4,17].…”

“…In JF-V1.0, as in most previous applications of ECMC, only a single independent point mass is active. The ECMC dynamics is thus very simple, yet it mixes and relaxes at a rate at least as fast as in molecular dynamics [19,23,24]. Third, ECMC by construction exactly samples the Boltzmann (canonical) distribution, whereas molecular dynamics is in principle micro-canonical, that is, energy-conserving.…”

Event-Chain Monte Carlo: Foundations, Applications, and Prospects

“…factor field (44) The factor field of Equation ( 44) may be added and its linear parameter a adjusted to any pair-factor potential. Attractive factor fields may thus be added to hard-sphere factors or to Lennard-Jones factors [55]. With the linear factor adjusted to compensate the virial pressure, O(N 3/2 ) autocorrelation times [rather than O(N 2 ) without factor fields] and O(N 2 ) mixing times [rather than O(N 2 log N)] are found.…”

“…With the linear factor adjusted to compensate the virial pressure, O(N 3/2 ) autocorrelation times [rather than O(N 2 ) without factor fields] and O(N 2 ) mixing times [rather than O(N 2 log N)] are found. One particular feature of event-chain dynamics at the optimal value of the factor field is that the chains have zero linear drift, and therefore also vanishing virial pressure [8,55].…”

Large-scale dynamics of event-chain Monte Carlo

“…The slowest mode generally relaxes on a time scale τ which depends on the system size L as τ ∼ L z . For N -particle systems in one spatial dimension (1D), ECMC can be analyzed in great detail [17,18] and compared to molecular dynamics and to the reversible local Metropolis algorithm. The autocorrelation functions of density fluctuations in ECMC, as in molecular dynamics, are characterized by a dynamic exponent z = 1, where the unit of time corresponds to a sweep of N moves or events.…”