Nonperiodic ising quantum chains and conformal invariance

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.