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

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

1997-09-26

arxiv.org/abs/cond-mat/9709303v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 1 figure, submitted to Physica A

Scientific paper

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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