Li Nishikawa et al 2022

From Werner KRAUTH

Jump to: navigation, search

B. Li, Y. Nishikawa, P. Hoellmer, L. Carillo, A. C. Maggs, W. Krauth A. C. Maggs, W. Krauth Hard-disk computer simulations -- a historic perspective arXiv:2207.07715 (2022)

Abstract We discuss historic pressure computations for the hard-disk model performed since 1953, and compare them to results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental effort to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository.

NB: The open-source repository is under construction. We expect it to open to the public in August 2022.

Electronic version (from arXiv)

Personal tools