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Three simple scenarios for high-dimensional sphere packings.

Publication ,  Journal Article
Charbonneau, P; Morse, PK; Perkins, W; Zamponi, F
Published in: Physical review. E
December 2021

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.

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Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

December 2021

Volume

104

Issue

6-1

Start / End Page

064612

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
 

Citation

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Charbonneau, P., Morse, P. K., Perkins, W., & Zamponi, F. (2021). Three simple scenarios for high-dimensional sphere packings. Physical Review. E, 104(6–1), 064612. https://doi.org/10.1103/physreve.104.064612
Charbonneau, Patrick, Peter K. Morse, Will Perkins, and Francesco Zamponi. “Three simple scenarios for high-dimensional sphere packings.Physical Review. E 104, no. 6–1 (December 2021): 064612. https://doi.org/10.1103/physreve.104.064612.
Charbonneau P, Morse PK, Perkins W, Zamponi F. Three simple scenarios for high-dimensional sphere packings. Physical review E. 2021 Dec;104(6–1):064612.
Charbonneau, Patrick, et al. “Three simple scenarios for high-dimensional sphere packings.Physical Review. E, vol. 104, no. 6–1, Dec. 2021, p. 064612. Epmc, doi:10.1103/physreve.104.064612.
Charbonneau P, Morse PK, Perkins W, Zamponi F. Three simple scenarios for high-dimensional sphere packings. Physical review E. 2021 Dec;104(6–1):064612.

Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

December 2021

Volume

104

Issue

6-1

Start / End Page

064612

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering