Anisotropic Scaling in Layered Aperiodic Ising Systems
B. Berche (1), P.E. Berche (1), M. Henkel (2), F. Igloi (3,4), P., Lajko (4), S. Morgan (2), L. Turban (1) ((1) Henri Poincare University,, Nancy, (2) Oxford University, (3) Research Institute for Solid State Physics,, Budapest, (4) University of Szeged)
TL;DR
This paper investigates how layered aperiodic modulations affect the critical behavior of 2D Ising models, revealing induced anisotropic scaling and continuous variation of the anisotropy exponent with modulation strength.
Contribution
It demonstrates that aperiodic layering causes anisotropic scaling and that the anisotropy exponent varies continuously, showing scale invariance without conformal invariance at criticality.
Findings
Aperiodicity induces anisotropic scaling in 2D Ising systems.
The anisotropy exponent z varies with modulation amplitude.
Systems are scale invariant but not conformally invariant at criticality.
Abstract
The influence of a layered aperiodic modulation of the couplings on the critical behaviour of the two-dimensional Ising model is studied in the case of marginal perturbations. The aperiodicity is found to induce anisotropic scaling. The anisotropy exponent z, given by the sum of the surface magnetization scaling dimensions, depends continuously on the modulation amplitude. Thus these systems are scale invariant but not conformally invariant at the critical point.
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