title: Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.
abstract: The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 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 ϕ∼d2(-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.
authors.affiliation: Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
authors.forename: Yuliang
authors.initials: Y
authors.lastname: Jin
authors.forename: Patrick
authors.initials: P
authors.lastname: Charbonneau
authors.forename: Sam
authors.initials: S
authors.lastname: Meyer
authors.forename: Chaoming
authors.initials: C
authors.lastname: Song
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi
mesh_terms: D008962:Models, Theoretical; D011336:Probability; D013816:Thermodynamics