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A zero-field Ising model with ferromagnetic coupling constants on theso-called Labyrinth tiling is investigated. Alternatively, this can be regardedas an Ising model on a square lattice with a quasi-periodic distribution of upto eight different coupling constants. The duality transformation on thistiling is considered and the self-dual couplings are determined. Furthermore,we analyze the subclass of exactly solvable models in detail parametrizing thecoupling constants in terms of four rapidity parameters. For those, theself-dual couplings correspond to the critical points which, as expected,belong to the Onsager universality class.Comment: 25 pages, 6 figure

A CRITICAL ISING MODEL ON THE LABYRINTH