Counterintuitive ground states in soft-core models

TL;DR

This paper reveals that certain soft-core models, like the Gaussian core model, have unexpectedly complex and non-traditional ground states in low to moderate dimensions, challenging previous conjectures.

Contribution

It disproves the conjecture that dilute ground states are Bravais lattices in dimensions 2 to 8, showing existence of lower-energy non-Bravais lattices in dimensions 5 and 7.

Findings

Non-Bravais lattices have lower energy than predicted in dimensions 5 and 7.

Disproves previous conjecture about ground state structures in soft-core models.

Highlights complex behavior of soft-core models in low to moderate dimensions.

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.