Séminaire du LPTMS: Werner Krauth (LPENS)

Fast irreversible Markov chains in statistical physics

Werner Krauth (LPENS)

The Monte Carlo method is an outstanding computational tool in science. Since its origins, it has relied on the detailed-balance condition (that is, the absence of flows in equilibrium) to map general computational problems onto equilibrium-statistical-physics systems.

Irreversible Markov chains violate the detailed-balance condition. They realize the equilibrium Boltzmann distribution as a steady state with non-vanishing flows. For one-dimensional particle models we have proven rigorously that local algorithms reach equilibrium on much faster time scales than the reversible algorithms that satisfy detailed balance. The event-chain Monte Carlo algorithm (ECMC) generalizes these irreversible Markov chains to higher dimensions. It relies on a factorized Metropolis filter which is based on a consensus rule rather than on an energy criterion.

As applications I will discuss the solution of the famous two-dimensional melting problem for hard disks and related systems, where we showed, using ECMC, that hard disks melt neither following the Kosterlitz-Thouless-Halperin-Nelson-Young prescription nor the alternative first-order liquid-solid scenario. I will also present the use of ECMC for the general classical all-atom N-body problem. Here, the Boltzmann distribution exp(-beta E) is sampled (without any discretization or truncation error) but the potential energy E remains unknown. This is of great interest in the Coulomb problem, where E or its derivatives, the forces, are hard to compute. Our recent JeLLyFysh open-source Python application implements ECMC for models from hard spheres to three-dimensional water systems. I will finish by discussing its features, that closely mirror the mathematical formulation of ECMC, and by presenting its future challenges.


Date/Time : 01/10/2019 - 11:00 - 12:00

Location : Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530

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