2008/11/30 by Henry Cohn, Abhinav Kumar · 1 citation
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math.MG
paper · pdf · doi:10.1103/physreve.78.061113
published as Physical Review E 78, 061113 (2008) · 7 pages, 4 figures, appeared in Physical Review E (http://pre.aps.org/)
openalex publication_date 2008/12/12 · arxiv created 2008/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.