2006/06/30 by Helen Au-Yang, Jacques H. H. Perk · 15 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Antiferromagnetism #Aperiodic graph #Combinatorics #Condensed matter physics #Ferromagnetism #Fibonacci number #Invariant (physics) #Ising model #Lattice (music) #Mathematical physics #Mathematics #Physics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-006-9213-9
published in Journal of Statistical Physics 127(2), 265-286 (Springer Science+Business Media) · LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints corrected
arxiv created 2006/12/29 · openalex publication_date 2007/02/09 · arxiv updated 2011/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the q-dependent susceptibility chi(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 chi(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.