ECMC 2021 Hoellmer

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Dipole rotations in non-reversible Markov Chains

Philipp Höllmer , A. C. Maggs, Werner Krauth

Bethe Center for Theoretical Physics, University of Bonn, Bonn (Germany)

CNRS UMR7083, ESPCI Paris, PSL Research University, Paris (France)

Laboratoire de Physique de l’Ecole normale supérieure, Paris (France)

Abstract In recent years, several algorithms belonging to the family of event-chain Monte Carlo (ECMC) have been proposed. They share the concept of particle and displacement lifting where an active particle is displaced on a non-interacting trajectory in a lifted direction. The individual algorithms differ, however, in the update scheme of the lifting variables in the events that are required to construct a non-reversible continuous time Markov chain. We study straight ECMC with direction sweeps, reflective ECMC, Newtonian ECMC, and forward ECMC for many simplified two-dimensional extended flexible dipoles that resemble water molecules in the context of molecular simulation models. Here, we point out possible pitfalls of the straight and reflective versions. We show that the dynamics of the polarization of many dipoles are analogous to a simple Gaussian random walk and a path integral. The polarization's integrated autocorrelation times show that straight ECMC, which was the superior variant for the problem of two-dimensional hard disks, rotates the dipoles slowly in comparison to the other methods. In comparison to a reversible Metropolis algorithm, the optimal ECMC algorithm yields a speedup that increases for lower densities up to a factor of $60$, which thus motivates its application to systems of long-range interacting extended molecules at the core of the JeLLyFysh project.

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