Hard-disk packings, fast Markov chains, and the two phase transitions of two-dimensional particle systems

Werner Krauth (ENS Paris)

Jan 20. 2022, 15:00 — 15:40

In the hard-disk model, packings exist from the sparse  limit (Böröczky, 1964) up to the proven close packing  (Fejes, 1940). In the context of local non-reversible Markov chains, we have recently proposed escape times from relaxed Böröczky packings as poor man's versions of mixing times.  The fastest Markov chains correspond to the non-reversible event-chain Monte Carlo algorithms that have allowed us to characterize the two phase transitions in two-dimensional particle systems, between the liquid and the hexatic and between the hexatic and the solid phases. In this talk, I will introduce to these concepts at the interface between mathematics and statistical physics.

* P. Hoellmer, N. Noirault, B. Li, A. C. Maggs, W. Krauth Sparse hard-disk packings and local Markov chains arXiv:2109.13343 (2021)
* W. Krauth Event-Chain Monte Carlo: Foundations, Applications, and Prospects Frontiers in Physics 9 229 (2021)
* S. C. Kapfer, W. Krauth, Soft-disk melting: From liquid-hexatic coexistence to continuous transitions Physical Review Letters 114, 035702 (2015)
* E. P. Bernard, W. Krauth, First-order liquid-hexatic transition in hard disks Physical Review Letters 107, 155704 (2011)

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Optimal Point Configurations on Manifolds (Workshop)
Christine Bachoc (U Bordeaux)
Henry Cohn (Microsoft, Redmond)
Peter Grabner (TU Graz)
Douglas Hardin (Vanderbilt U, Nashville)
Edward Saff (Vanderbilt U, Nashville)
Achill Schürmann (U of Rostock)
Robert Womersley (UNSW, Sydney)