Jin, Y; Charbonneau, P; Meyer, S; Song, C; Zamponi, F, *Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings.*,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 82 no. 5 Pt 1
(November, 2010),
pp. 051126 [repository], [doi] .
**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.*