Selfduality for coupled Potts models on the triangular lattice

TL;DR

This paper develops selfdual solutions for coupled Potts models on the triangular lattice using duality and loop model mappings, revealing new critical points and including three-spin couplings for selfduality.

Contribution

It introduces a novel loop model approach that surpasses previous methods, enabling the inclusion of three-spin couplings for selfdual coupled Potts models.

Findings

Identification of new critical points for coupled models

Loop model mapping proves more effective than duality-decimation

Three-spin couplings are essential for selfduality in coupled models

Abstract

We present selfdual 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 to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points.