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

We introduce a class of 2d Ising models with aperiodic modulations of the c oupling constants following a 2d substitution rule. The relevance of the ap eriodicity to the phase transition is examined through an approximative rea l 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 . (C) 2000 Elsevier Science B.V. All rights reserved.