Self-duality for coupled Potts models on the triangular lattice

Abstract

We present self-dual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows us to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating self-dual solutions. A numerical study of the case of two coupled, models leads to the identification of novel critical points.