Communications in Mathematical Physics

, Volume 129, Issue 3, pp 599–619 | Cite as

Weak matching rules for quasicrystals

  • Joshua E. S. Socolar


Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in “perp-space” are uniformly bounded. It is shown here that weak matching rules exist forN-fold symmetric tilings, whereN is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules forN-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Joshua E. S. Socolar
    • 1
  1. 1.Department of PhysicsHarvard UniversityCambridgeUSA

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