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

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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics 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 ∼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.

Original languageEnglish (US)
Article number051126
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - Nov 18 2010
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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