New duality relations for classical ground states |
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Authors: | Torquato S Stillinger F H |
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Affiliation: | School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA. |
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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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