A CLASSIFICATION OF CRITICAL PHENOMENA ON QUASI-CRYSTALS AND OTHER APERIODIC STRUCTURES

We investigate statistical-mechanical models on aperiodic structures ( e.g. quasi-periodic, random, self-similar). We derive a condition for the relevance of any kind of aperiodicity near a continuous phase tran sition, in the spirit of the Harris criterion. This explains why cryst als and quasi-crystals exhibit the same critical behaviour. Novel univ ersality classes of critical phenomena are predicted on structures wit h unbounded geometrical fluctuations, whenever their wandering exponen t exceeds a model-dependent threshold value.