New Duality Relations for Classical Ground States
Abstract
We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the nature of the ground states of long-ranged potentials and vice versa. They also lead to bounds on the T=0 system energies in density intervals of phase coexistence, the identification of a one-dimensional system that exhibits an infinite number of ``phase transitions," and a conjecture regarding the ground states of purely repulsive monotonic potentials.
Cite
@article{arxiv.0710.5315,
title = {New Duality Relations for Classical Ground States},
author = {S. Torquato and F. H. Stillinger},
journal= {arXiv preprint arXiv:0710.5315},
year = {2009}
}
Comments
11 pages, 2 figures. Slightly revised version that corrects typos. This article will be appearing in Physical Review Letters in a slightly shortened form