Exact solution of solid-on-solid models for twisted affine Lie algebras A 2 n(2) and A 2 n−1 (2)

Abstract

We report new exact solutions of restricted and unrestricted solid-on-solid (SOS) models associated with the twisted affine Lie algebras X n (2) = A 2 n (2) and A 2 n−1 (2). The Boltzmann weights are parametrized by elliptic theta functions and fulfill the Yang-Baxter equation. The trigonometric case of the solutions corresponds to the SOS counterpart of the solvable vertex models arising from the X n (2) quantum R-matrices. The restricted models (RSOS) are labeled by the level l as well as the rank n. We show that the level- l A 2 n−1 (2) RSOS model is equivalent to the level- n C l (1) RSOS model, which is a manifestation of the level-rank duality. One-point functions of the A 2 n−1 (2) RSOS model are obtained by using the coset pair C n (1) ⊕ A 2 n−1 (1) ⊃ C n (1). We also determine the one-point functions of the X n (2) vertex models in terms of X n (2) string functions.