%0 Journal Article
%T Hard-disk pressure computations—a historic perspective
%+ Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023))
%+ Laboratoire Charles Coulomb (L2C)
%+ Department of Quantum Engineering and Systems Science, Graduate School of Engineering The University of Tokyo
%+ Physikalisches Institut [Bonn]
%+ Bethe Center for Theoretical Physics (BCTP)
%+ Gulliver (UMR 7083)
%+ Systèmes Classiques ou Quantiques en Interaction
%A Li, Botao
%A Nishikawa, Yoshihiko
%A Höllmer, Philipp
%A Carillo, Louis
%A Maggs, A. C.
%A Krauth, Werner
%Z 21 pages, 13 figures, open-source repository
%< avec comité de lecture
%@ 0021-9606
%J Journal of Chemical Physics
%I American Institute of Physics
%V 157
%N 23
%P 234111
%8 2022-12-21
%D 2022
%Z 2207.07715
%R 10.1063/5.0126437
%Z Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Journal articles
%X We discuss pressure computations for the hard-disk model performed since 1953 and compare them to the 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 efforts 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.
%G English
%L hal-03735825
%U https://hal.science/hal-03735825
%~ ENS-PARIS
%~ ESPCI
%~ CNRS
%~ PARISTECH
%~ GULLIVER
%~ L2C
%~ INC-CNRS
%~ PSL
%~ MIPS
%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ LPENS
%~ UNIV-PARIS
%~ UNIVERSITE-PARIS
%~ UP-SCIENCES
%~ ENS-PSL
%~ ESPCI-PSL
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021
%~ TEST2-HALCNRS