Yang-Baxter integrable dimers on a strip

Abstract

The dimer model on a strip is considered as a Yang-Baxter integrable six vertex model at the free-fermion point with crossing parameter &lambdal = π/2 and quantum group invariant boundary conditions. A one-to-many mapping of vertex onto dimer configurations allows for the solution of the free-fermion model to be applied to the anisotropic dimer model on a square lattice where the dimers are rotated by 45° compared to their usual orientation. In a suitable gauge, the dimer model is described by the Temperley-Lieb algebra with loop fugacity β = 2 COS λ = 0. It follows that the model is exactly solvable in geometries of arbitrary finite size. We establish and solve transfer matrix inversion ide..