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arXiv:cond-mat/9711096 · Physical review. B, Condensed matter

Surface properties of aperiodic Ising quantum chains

Joachim Hermisson, Uwe Grimm

Published Jan 1, 1998• 12 citations
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Abstract

We consider Ising quantum chains with a quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behavior of several bulk and surface quantities is obtained by exact real-space renormalization.
DOI
10.1103/physrevb.57.r673

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We study the surface magnetization and critical behavior of a hierarchical quantum Ising chain. The surface magnetization exponent ${\mathrm{\ensuremath{\beta}}}_{\mathit{s}}$ is calculated exactly by using scaling arguments. It is found that, although the size of the fluctuations in the exchange couplings may be bounded or unbounded depending on the value of the hierarchical parameter r, the surface critical behavior stays nonuniversal with ${\mathrm{\ensuremath{\beta}}}_{\mathit{s}}$ varying continuously with the value of r. This result is rather different from the cases where the aperiodicity of the couplings is generated by substitution rules and different types of critical behavior are observed for bounded and unbounded fluctuations in the couplings.
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