# 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

#### Upcoming seminars

- Soutenance de thèse: Mathieu Isoard - 10 Sep 2020 - 14:00
- Séminaire du LPTMS : David Zwicker - 10 Nov 2020 - 11:00