Abstract
Hamiltonians for nonperiodic tilings are considered. It is shown that the quasicrystalline tiling obtained by the cut-and-strip method from aD-dimensional cubic lattice may bs a ground state only if the tiling possesses a high orientational symmetry: the (2,D)-quasicrystal should haveD-fold symmetry ifD is even and 2D-fold symmetry ifD is odd. For interactions of a finite range the restrictions are stronger: only a (2, 5)-quasicrystal (Penrose tiling) may be a stable ground state.
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Burkov, S.E. Ground states of two-dimensional quasicrystals. J Stat Phys 52, 453–461 (1988). https://doi.org/10.1007/BF01016426
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DOI: https://doi.org/10.1007/BF01016426