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

Abstract

12 pages, 7 figuresThe isostatic jamming limit of frictionless spherical particles from Edward's statistical mechanics [Song et al. Nature (2008)] is generalized to arbitrary dimension $d$. An asymptotic high-dimensional behavior 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 are consistent with a growing accuracy of the theory with dimension