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arXiv · 0710.5315

New Duality Relations for Classical Ground States

S. Torquato·F. H. Stillinger
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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.

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S. Torquato, F. H. Stillinger. 2008-01-14. New Duality Relations for Classical Ground States. https://doi.org/10.1103/physrevlett.100.020602

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