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New Duality Relations for Classical Ground States

Authors
  • Torquato, S.
  • Stillinger, F. H.
Type
Preprint
Publication Date
Jan 14, 2008
Submission Date
Oct 28, 2007
Identifiers
DOI: 10.1103/PhysRevLett.100.020602
Source
arXiv
License
Unknown
External links

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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