Gutzwiller Colloquium: Two-dimensional melting: New algorithms, new insights

Date

Feb 7, 2018

Time

4:30 PM - 5:30 PM

Speaker

Werner Krauth

Affiliation

Laboratoire de Physique Statistique, Ecole Normale Sup rieure, Paris, and Director of Research at the CNRS, France

Language

en

Main Topic

Physik

Other Topics

Physik

Description

The hard-disk model has exerted outstanding influence on computational physics and statistical mechanics. Decades ago, hard disks were the first system to be studied by reversible Markov-chain Monte Carlo methods satisfying the detailed-balance condition and by molecular dynamics. It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur even though homogeneous short-range interacting particle systems cannot develop crystalline order. Analysis of the system was made difficult by the absence of powerful simulation methods. In recent years, we have developed a class of irreversible event-chain Monte Carlo algorithms that violate detailed balance. They realize thermodynamic equilibrium as a steady state with non-vanishing probability flows. A new factorized Metropolis filter turns them into a paradigm for general Monte Carlo calculations. I will in particular show how the event-chain Monte Carlo algorithm has allowed us to demonstrate that hard disks melt with a first-order transition from the liquid to the hexatic and a continuous transition from the hexatic to the solid. Event-chain computations have also lead to our new understanding of two-dimensional melting for soft disks, that has been intensely studied in experiment. Finally, I will discuss two-dimensional melting on a substrate (as it is realized in skyrmion systems), and for active particles, and will present a very recent application of the event-chain algorithm to Coulomb-type long-range-interacting systems.

Last modified: Feb 7, 2018, 9:04:41 AM