Strong-disorder renormalization group study of aperiodic quantum Ising chains

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 fluctu...

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Bibliographic Details
Published in:Journal of statistical mechanics 2012-03, Vol.2012 (3), p.1-32
Main Authors: Oliveira Filho, Fleury J, Faria, Maicon S, Vieira, Andre P
Format: Article
Language:English
Subjects:
Asymptotic properties
Couplings
Exponents
Fluctuation
Ising model
Magnetization
Mathematical analysis
Statistical mechanics
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Summary: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.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2012/03/P03007