Critical Behavior of Hierarchical Ising Models

Details Critical Behavior of Hierarchical Ising Models Critical Behavior of Hierarchical Ising Models

1995-06-22

arxiv.org/abs/cond-mat/9506100v1

Physics

Condensed Matter

21 pages, plain TeX, 3 figures available on request, to appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.52.7159

We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or marginal. For marginal sequences we have performed a detailed study, which involved analytical and numerical calculations of different surface and bulk critical quantities in the two-dimensional classical as well as in the one-dimensional quantum version of the model. The critical exponents are found to vary continuously with the strength of the modulation, while close to the critical point the system is essentially anisotropic: the correlation length is diverging with different exponents along and perpendicular to the layers.

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