Glass transition and random close packing above three dimensions

Patrick Charbonneau, Atsushi Ikeda, Giorgio Parisi, Francesco Zamponi

Published 2011-07-23, updated 2011-10-27Version 3

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.