Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1999-02-12
Int. J. Mod. Phys. B 8 (1994) 3579-3600
Nonlinear Sciences
Exactly Solvable and Integrable Systems
25 pages, 6 figures
Scientific paper
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 couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.
Baake Michael
Baxter R. J.
Grimm Uwe
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