We employ an adaptation of a strong-disorder renormalization-group techniquein order to analyze the ferro-paramagnetic quantum phase transition of Isingchains with aperiodic but deterministic couplings under the action of atransverse field. In the presence of marginal or relevant geometricfluctuations induced by aperiodicity, for which the critical behavior isexpected to depart from the Onsager universality class, we derive analyticaland asymptotically exact expressions for various critical exponents (includingthe correlation-length and the magnetization exponents, which are not easilyobtainable by other methods), and shed light onto the nature of the groundstate structures in the neighborhood of the critical point. The main resultsobtained by this approach are confirmed by finite-size scaling analyses ofnumerical calculations based on the free-fermion method.
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