New duality relations for classical ground states

S. Torquato, F. H. Stillinger

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish (US)
Article number020602
JournalPhysical review letters
Issue number2
StatePublished - Jan 17 2008

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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