In search of multipolar order on the Penrose tiling
نویسندگان
چکیده
Based on Monte Carlo calculations, multipolar ordering on the Penrose tiling, relevant for twodimensional molecular adsorbates on quasicrystalline surfaces and for nanomagnetic arrays, has been analyzed. These initial investigations are restricted to multipolar rotors of rank one through four—described by spherical harmonics Ylm with l = 1 . . . 4 and restricted to m = 0—positioned on the vertices of the rhombic Penrose tiling. At first sight, the ground states of odd-parity multipoles seem to exhibit long-range order, indicated by the appearance of a superstructure in the form of the decagonal Hexagon-Boat-Star tiling, in agreement with previous investigations of dipolar systems. Yet careful analysis establishes that long-range order is absent in all cases investigated here, and only short-range order exists. This result should be taken as a warning for any future analysis of order in either real or simulated arrangements of multipoles on quasiperiodic templates.
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