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 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.Comment: 13 pages, 7 figure