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Center for Nonlinear Studies |
Regular (Bravais) lattices have always been an important special case for the high-dimensional sphere packing problem. While we are used to think of lattices in low dimensions as highly ordered, lattices in high dimensions can be extraordinarily complex, and, surprisingly, disordered. Searching the space of n-dimensional lattices for good sphere packing lattices is a hard problem, which displays a lot of the same physics as the hard-sphere fluid: we observe a "crystallization" transition in equilibrium, a metastable fluid phase, and a random close packing ensemble with its own critical exponents.
Host: Aric Hagberg