Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions

S. T. R. Pinho; T. A. S. Haddad; S. R. Salinas

doi:10.1016/s0378-4371(98)00185-x

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arXiv · cond-mat/9709303

Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions

S. T. R. Pinho·T. A. S. Haddad·S. R. Salinas

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Abstract

We write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuations.

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BibTeX RIS

S. T. R. Pinho, T. A. S. Haddad, S. R. Salinas. 1997-09-26. Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions. https://doi.org/10.1016/s0378-4371(98)00185-x

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