Abstract
In a recent paper, Luck investigated the critical behavior of one-dimensional Ising quantum chains with coupling constants modulated according to general nonperiodic sequences. In this note, we take a closer look at the case where the sequences are obtained from (two-letter) substituion rules and at the consequences of Luck's results at criticality. They imply that only for a certain class of substitution rules is the long-distance behavior still described by thec=1/2 conformal field theory of a free Majorana fermion as for the periodic Ising quantum chain, whereas the general case does not lead to a conformally invariant scaling limit.
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Grimm, U., Baake, M. Nonperiodic ising quantum chains and conformal invariance. J Stat Phys 74, 1233–1245 (1994). https://doi.org/10.1007/BF02188226
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DOI: https://doi.org/10.1007/BF02188226