Classification of particle numbers with unique Heitmann-Radin minimizer

created by deluca on 30 Jan 2017
modified on 21 Sep 2017

[BibTeX]

Published Paper

Inserted: 30 jan 2017
Last Updated: 21 sep 2017

Journal: J. Stat. Phys.
Volume: 167
Number: 6
Pages: 1586--1592
Year: 2017

Abstract:

We show that minimizers of the Heitmann-Radin energy \cite{HR} are unique if and only if the particle number $N$ belongs to an infinite sequence whose first thirty-five elements are 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120 (see the paper for a closed-form description of this sequence). The proof relies on the discrete differential geometry techniques introduced in \cite{DLF}.