Abstract. 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.arXiv:1112.5141v2 [cond-mat.stat-mech]

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

We performed Monte Carlo simulations to investigate the steadystate critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

No abstract