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.

11 pages, 2 figures. Slightly revised version that corrects typos. This article will be appearing in Physical Review Letters in a slightly shortened form

References in corpus (6)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Universally optimal distribution of points on spheres
• Fluid and solid phases of the Gaussian core model
• Soft Spheres Make More Mesophases
• Collective Coordinate Control of Density Distributions
• Crystalline ground states for classical particles

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