Triangular Potts Model at its Transition Temperature, and Related Models

Kelland has solved a restricted ice-type model on the triangular lattice. Here it is shown that this is equivalent to a restricted six-vertex model on the Kagomé lattice, and to the g-state triangular (or hexagonal) Potts model at its transition temperature Tc. This enables us to obtain the free energy, internal energy and latent heat of the Potts model at Tc. The relation of this work to the operator method of Temperley and Lieb is explained, and this method is used to consider a generalized triangular Potts model which includes a three-site interaction on alternate triangles. It is shown that this model is self-dual. The results for the bond percolation problem on the triangular lattice give an excellent verification of series expansion predictions.