Triangular Potts model at its transition temperature, and related models

Abstract

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 Kagome lattice, and to the $q$-state triangular (or hexagonal) Potts model at its transition temperature $T$$_{\text{c}}$. This enables us to obtain the free energy, internal energy and latent heat of the Potts model at $T$$_{\text{c}}$. 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.