Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
arXiv:cond-mat/9709303 · doi:10.1016/S0378-4371(98)00185-X
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.
9 pages, 1 figure, submitted to Physica A