Renormalization of two-dimensional Ising systems with irrelevant, marginal and relevant aperiodic (dis)order

We introduce a class of 2d Ising models with aperiodic modulations of the coupling constants following a 2d substitution rule. The relevance of the aperiodicity to the phase transition is examined through an approximative real space renormalization group approach known as the cumulant approximation. We find that the relevance of the aperiodic disorder is determined by the fluctuations of the mean coupling as predicted by the Harris–Luck criterion.