  We employ an adaptation of a strong-disorder renormalization-group technique
in order to analyze the ferro-paramagnetic quantum phase transition of Ising
chains with aperiodic but deterministic couplings under the action of a
transverse field. In the presence of marginal or relevant geometric
fluctuations induced by aperiodicity, for which the critical behavior is
expected to depart from the Onsager universality class, we derive analytical
and asymptotically exact expressions for various critical exponents (including
the correlation-length and the magnetization exponents, which are not easily
obtainable by other methods), and shed light onto the nature of the ground
state structures in the neighborhood of the critical point. The main results
obtained by this approach are confirmed by finite-size scaling analyses of
numerical calculations based on the free-fermion method.
