title: 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.
authors.affiliation: School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA.
authors.forename: S
authors.initials: S
authors.lastname: Torquato
authors.forename: F H
authors.initials: FH
authors.lastname: Stillinger