Critical behavior of a class of noncommutative aperiodic models on hierarchical lattices

We propose two schemes to construct aperiodic spin models on hierarchical lattices. As in previous works, we choose nearest-neighbor exchange interactions according to a substitution rule. In contrast to these works, however, we are able to deal with Thue–Morse substitutions, a→ab, b→ba, where the geometrical fluctuations are due to the noncommutative nature of the letter sequences. For the Ising case, we show some examples where the critical behavior belongs to the same universality class of the underlying uniform system.