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)