  It is well known that statistical mechanics systems exhibit subtle behavior
in high dimensions. In this paper, we show that certain natural soft-core
models, such as the Gaussian core model, have unexpectedly complex ground
states even in relatively low dimensions. Specifically, we disprove a
conjecture of Torquato and Stillinger, who predicted that dilute ground states
of the Gaussian core model in dimensions 2 through 8 would be Bravais lattices.
We show that in dimensions 5 and 7, there are in fact lower-energy non-Bravais
lattices. (The nearest three-dimensional analog is the hexagonal close-packing,
but it has higher energy than the face-centered cubic lattice.) We believe
these phenomena are in fact quite widespread, and we relate them to
decorrelation in high dimensions.
