A CRITICAL ISING-MODEL ON THE LABYRINTH

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual coupling s are determined. Furthermore, we analyze the subclass of exactly solv able models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspo nd to the critical points which, as expected, belong to the Onsager un iversality class.