Abstract
Necessary conditions for a quasicrystal to be a ground state are found within the framework of a tiling model (thermal fluctuations are supposed to be irrelevant). It is proven that a generic quasicrystal cannot be a ground state. Only very special quasicrystals are shown to survive: They must possess high rotational symmetry or the frequencies defining quasiperiodic properties must satisfy numerous rational constraints. A quasicrystal may be a ground state only if hexagons flipping under the infinitesimal phason shift are not isolated from one another but form rows or nets. Necessary and sufficient conditions for a (2,3) quasicrystal to be a ground state are found. All (2,4) quasicrystals satisfying the necessary conditions are classified. Stability of a quasicrystalline phase is discussed.
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