In search of multipolar order on the Penrose tiling

E. Y. Vedmedenko, S. Even Dar Mandel, R. Lifshitz

Research output: Contribution to journalArticlepeer-review


We use Monte Carlo calculations to analyse multipolar ordering on the Penrose tiling, relevant for two-dimensional molecular adsorbates on quasicrystalline surfaces and for nanomagnetic arrays. Our 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, in agreement with previous investigations of dipolar systems. Yet, careful analysis performed here establishes that, despite earlier claims, long-range order is absent for all types of rotors, and only short-range order exists. Nevertheless, we show here that short-range order suffices to yield a superstructure in the form of the decagonal Hexagon-Boat-Star tiling. Our results should be taken as a warning for any future analysis of order in either real or simulated arrangements of multipoles on quasiperiodic templates.

Original languageEnglish
Pages (from-to)2197-2207
Number of pages11
JournalPhilosophical Magazine
Issue number13-15
StatePublished - May 2008


  • Adsorption
  • Magnetic order
  • Magnetism
  • Multipolar order
  • Order
  • Quasicrystals
  • Surface physics


Dive into the research topics of 'In search of multipolar order on the Penrose tiling'. Together they form a unique fingerprint.

Cite this