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Application of Edwards' statistical mechanics to high dimensional jammed sphere packings

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Yuliang Jin, Patrick Charbonneau, Sam Meyer, Chaoming Song, Francesco Zamponi

Statistical Mechanics · Submitted 2 Sep 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These numerical results support a growing accuracy of the theoretical approach with dimension.

how it is stated · hedged possibility 0.72 read the record →

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arXiv ID1009.0546 (version 3)
Pith IDVZHKU5LP, Pith's permanent record of this paper and its review
CitationChaoming Song, Francesco Zamponi, Patrick Charbonneau, Sam Meyer, Yuliang Jin. "Application of Edwards' statistical mechanics to high dimensional jammed sphere packings." arXiv:1009.0546 (2010). https://pith.science/paper/VZHKU5LP
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,964 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $\phi\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. contribution 1.00 0.78 0.27 asserted 1.00
s1 The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. method 0.96 0.92 0.06 asserted 1.00
s2 The resulting random close packing density scaling $\phi\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. result 0.96 0.73 0.48 hedged possibility 0.85
s3 The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. method 0.80 0.82 0.07 asserted 0.96
s4 These numerical results support a growing accuracy of the theoretical approach with dimension. interpretation 0.82 0.85 0.20 hedged possibility 0.72
s5 The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings. future work 0.73 0.24 0.19 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.63.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song \emph{et al.}, Nature (London) {\bf 453}, 629 (2008)] is generalized to arbitrary dimension $d$ using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling $\phi\sim d\,2^{-d}$ is consistent with that of other approaches, such as replica theory and density functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

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