Inversion identities for inhomogeneous face models

Abstract

We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions using the underlying integrable structure and crossing properties of the local Boltzmann weights. For the critical restricted solid-on-solid (RSOS) models these identities together with some information on the analytical properties of the transfer matrix deter-mine the spectrum completely and allow to derive the Bethe equations for both periodic and general open boundary conditions.