NDLI: Duality relations for the classical ground states of soft-matter systems

Content Provider	Royal Society of Chemistry (RSC)
Author	Stillinger, F. H. Torquato, S. Zachary, Chase E.
Copyright Year	2011
Abstract	Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. In this paper, we extend the results of a recent letter [S. Torquato and F. H. Stillinger, Phys. Rev. Lett., 2008, 100, 020602] on duality relations for ground states of pair interactions to include three-body and higher-order functions. Our novel and general relations link the energy of configurations associated with a real-space potential to the corresponding energy of the dual (Fourier-transformed) potential and can be applied to ordered and disordered classical ground states. We use the duality relations to demonstrate how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the ground states of long-ranged potentials and vice versa. The duality relations also lead to bounds on the T = 0 system energies in density intervals of phase coexistence. Additionally, we identify classes of “self-similar“ potentials, for which one can rigorously relate low- and high-density ground-state energies. We analyze the ground state configurations and thermodynamic properties of a one-dimensional system expected to exhibit an infinite number of structural phase transitions and comment on the known ground states of purely repulsive monotonic potentials in the context of our duality relations.
Starting Page	3780
Ending Page	3793
Page Count	14
File Format	HTM / HTML PDF
ISSN	1744683X
Volume Number	7
Issue Number	8
Journal	Soft Matter
DOI	10.1039/c0sm01031f
Language	English
Publisher	Royal Society of Chemistry
Access Restriction	Open
Subject Keyword	Stillinger Classical mechanics Torquato Self-similarity
Content Type	Text
Resource Type	Article
Subject	Chemistry Condensed Matter Physics

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