Graphical approach to the nonintersecting string model: Star-triangle equation, inversion relation, and exact solution

A general q-state nonintersecting string model for q≧2 is studied, and solved, using a graphical approach. This model, of which special cases were first introduced by Strogonov and Schultz, has recently drawn further attention because of its relation to Potts models. In its simplest version, a uniform, separable nonintersecting string model on a quadratic lattice, it corresponds to a q2-state Potts model with Potts-spins on every other lattice face.