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Published April 8, 1985 | public
Journal Article Open

Mean-Field Theory of Quasicrystalline Order


A simple natural Landau theory of two- or three-component systems is described, which appears to give a region of the phase diagram in which quasicrystalline ordering is the state of lowest free energy. The quasicrystals are stabilized by special geometric relations between the length scales characterizing the components. Three components are required to stabilize a two-dimensional quasicrystal (a Penrose tiling) but two components suffice to stabilize an icosahedral three-dimensional quasicrystal.

Additional Information

©1985 The American Physical Society Received 7 February 1985 This work has been supported by the National Science Foundation through Grant No. DMR-83-14625 and through the Cornell Materials Science Center, Grant No. DMR-82-17227-A01. David DiVicenzo and James Sethna provided stimulation, advice, and encouragement at all stages, and we have benefitted from conversations with Tomas Bohe, Furrukh Khan, Paul Horn, Stellan Ostlund, Eric Siggia, and Paul Steinhardt.


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