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

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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.

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Authors and Affiliations

  1. Department of Physics, Oklahoma State University, Stillwater, OK, 74078-3072, USA

    Helen Au-Yang & Jacques H. H. Perk

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  1. Helen Au-Yang
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  2. Jacques H. H. Perk
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Supported in part by NSF Grant No. PHY 01-00.

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Au-Yang, H., Perk, J.H.H. Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models. J Stat Phys 127, 265–286 (2007). https://doi.org/10.1007/s10955-006-9213-9

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  • DOI: https://doi.org/10.1007/s10955-006-9213-9

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