New Duality Relations for Classical Ground States

S. Torquato and F. H. Stillinger

Phys. Rev. Lett. 100, 020602 – Published 17 January 2008

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.

Received 19 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.020602

Authors & Affiliations

S. Torquato

School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

F. H. Stillinger