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Journal of Statistical Physics

, Volume 127, Issue 2, pp 265–286 | Cite as

Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

  • Helen Au-Yang
  • Jacques H. H. Perk
Article

Abstract

We study the q-dependent susceptibility χ(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of χ(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic–antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.

Key Words

Ising model Z-invariance quasiperiodicity golden ratio silver mean correlation functions wavevector-dependent susceptibility 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Helen Au-Yang
    • 1
  • Jacques H. H. Perk
    • 1
  1. 1.Department of PhysicsOklahoma State UniversityStillwaterUSA

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