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Unusual Wetting Transitions in Two-Dimensional Quasi-Crystals

A model for wetting in a 2d ideal Penrose tiling is presented. The exponents and the nature of the wetting transition for long-ranged potentials are determined by an approximate renormalization group approach and confirmed numerically. The wetting shows unusual features due to the self-similarity of the quasi-periodic lattice. For short-ranged potentials a new universality class of transitions is established and the critical behaviour is determined.