Application of Edwards' statistical mechanics to high dimensional jammed sphere packings
arXiv:1009.0546 · doi:10.1103/PhysRevE.82.051126
Abstract
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 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 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.
13 pages, 7 figures
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