Counterintuitive ground states in soft-core models
arXiv:0811.1236 · doi:10.1103/PhysRevE.78.061113
Abstract
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.
7 pages, 4 figures, appeared in Physical Review E (http://pre.aps.org/)
References in corpus (15)
- Can Polymer Coils be modeled as "Soft Colloids"?
- Packing Hyperspheres in High-Dimensional Euclidean Spaces
- Universally optimal distribution of points on spheres
- Fluid and solid phases of the Gaussian core model
- Phase diagram of the Gaussian-core model
- Soap Froths and Crystal Structures
- Crystalline ground states for classical particles
- Amorphous packings of hard spheres in large space dimension
- Gaussian core model phase diagram and pair correlations in high Euclidean dimensions
- Hard Discs on the Hyperbolic Plane
- New Duality Relations for Classical Ground States
- From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces
- Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature
- Notions of denseness
- The D_4 root system is not universally optimal
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