Data from: Three simple scenarios for high-dimensional sphere packings

• Based on results from the physics and mathematics literature which suggest a series of clearly defined
  conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: in scenario A, crystallization is impeded and the glass phase constitutes the densest packing; in scenario B, crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible; and in scenario C, crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings for dimension d = 3-10 using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close packing tend to support scenario C. We additionally confirm that the crystal equation of state is dominated by the free-volume expansion and that a meaningful polynomial correction can be formulated. ... [Read More]

Total Size

2 files (12.9 MB)

Data Citation

• Charbonneau, P., Morse, P. K., Perkins, W., & Zamponi, F. (2021). Data from: Three simple scenarios for high-dimensional sphere packings. Duke Research Data Repository. https://doi.org/10.7924/r40z78x37

Creator

• Zamponi, Francesco
• Perkins, Will
• Charbonneau, Patrick
• Morse, Peter K.

DOI

• 10.7924/r40z78x37

Subject

• Cell-cluster expansion
• Phase transitions
• Frenkel-Ladd integration
• Statistical mechanics
• Mean-field theory
• Thermodynamics
• Crystallization
• Supercooled liquids

Publication Date

• December 9, 2021

ARK

• ark:/87924/r40z78x37

Affiliation

• Laboratoire de physique statistique, Ecole normale superieure, PSL Research University, Sorbonne Universites, Paris
• Physics
• Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
• Chemistry

Publisher

• Duke Research Data Repository

Type

• Dataset

Format

• TXT
• PY
• DAT
• M

Funding Agency

• Simons Foundation
• European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
• National Science Foundation

Grant Number

• National Science Foundation (Grant No. DMS-1847451, W.P.)
• European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 723955-GlassUniversality)
• Simons Foundation (Grant No. 454937, P.C., Grant No. 454955, F.Z.)

Contact

• Peter Morse, ORCID: 0000-0001-8950-3410, Email: peter.k.morse@gmail.com

License

• Creative Commons CC0 1.0 Universal

Title

• Data from: Three simple scenarios for high-dimensional sphere packings

License

• http://creativecommons.org/publicdomain/zero/1.0/

Repository

• Duke Research Data Repository