The hard-disk model has exerted outstanding influence on statistical physics, starting with the first ever Nbody calculation in science, by D. Bernoulli (1738), and leading up to its role in the very definition of statistical mechanics, by Maxwell and Boltzmann, and to the formal proof of the validity of statistical mechanics, by Sinai (1970). Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods (Metropolis et al, 1953) and by molecular dynamics (Alder and Wainwright, 1957). Up to the present day, the model is driving the development of algorithms (Bernard et al, 2009), including the "Beyond-Metropolis" approach (Michel et al, 2014). It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur (Alder and Wainwright, 1962) even though such systems cannot develop long-range crystalline order (Mermin and Wagner, 1966). This provided the starting point for the Kosterlitz-Thouless theory (1973). The hard-disk phase diagram was established only recently (Bernard and Krauth, 2011), thus providing a clear view on the physics of phase transitions in two dimensions, but still leaving many essential questions open.
The objective of this lecture series will thus be to discuss the aforementioned central topics of statistical physics from the unique vantage point of the hard-disk model, and in a self-contained way that will be accessible to a wide audience. Overall, the lecture series will introduce the approaches ranging from rigorous mathematics to statistics, and from the conception of algorithms and numerical simulations to the theory of phase transitions, to Kosterlitz-Thouless physics and to the interpretation of experiment. It is intended to show how the hard-disk model has continued to shape our view of the physical world, to teach us key aspects, and to prepare for general progress in science.
5 April 2017 (Wed) Hard Disks in Classical and Statistical Mechanics 1/2
6 April 2017 (Thu) Hard Disks in Classical and Statistical Mechanics 2/2
10 April 2017 (Mon) Hard Disks and Thermodynamic Phases
11 April 2017 (Tue) Hard Disks and Markov Chains
12 April 2017 (Wed) Hard Disks and Two-Dimensional Melting