Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings

James D. Sartor, Sean A. Ridout, and Eric I. Corwin
Phys. Rev. Lett. 126, 048001 – Published 26 January 2021
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Abstract

No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glasses and jamming is a mean-field theory which attempts to do so by working in the limit of infinite dimensions, such that correlations between neighbors are negligible. As such, results from this mean-field theory are not guaranteed to be observed in finite dimensions. However, many results in mean field for jamming have been shown to be exact or nearly exact in low dimensions. This suggests that the infinite dimensional limit is not necessary to obtain these results. In this Letter, we perform precision measurements of jamming scaling relationships between pressure, excess packing fraction, and number of excess contacts from dimensions 2–10 in order to extract the prefactors to these scalings. While these prefactors should be highly sensitive to finite dimensional corrections, we find the mean-field predictions for these prefactors to be exact in low dimensions. Thus the mean-field approximation is not necessary for deriving these prefactors. We present an exact, first-principles derivation for one, leaving the other as an open question. Our results suggest that mean-field theories of critical phenomena may compute more for ddu than has been previously appreciated.

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  • Received 7 July 2020
  • Revised 2 November 2020
  • Accepted 18 November 2020
  • Corrected 11 February 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.048001

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft Matter

Corrections

11 February 2021

Correction: A minor error in Eq. (12) has been fixed.

Authors & Affiliations

James D. Sartor1,*, Sean A. Ridout2,†, and Eric I. Corwin1,‡

  • 1Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
  • 2Department of Physics and Astronomy University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *Corresponding author. jsartor7@uoregon.edu
  • ridout@sas.upenn.edu
  • ecorwin@uoregon.edu

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Issue

Vol. 126, Iss. 4 — 29 January 2021

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