Inversion identities for inhomogeneous face models

TL;DR

This paper derives exact inversion identities for inhomogeneous IRF models, enabling complete spectral determination and Bethe equation derivation for critical RSOS models with various boundary conditions.

Contribution

It introduces a method to derive inversion identities for inhomogeneous IRF models, advancing spectral analysis and Bethe ansatz solutions.

Findings

Inversion identities are established for inhomogeneous IRF models.

These identities facilitate complete spectral characterization of critical RSOS models.

Bethe equations are derived for models with periodic and open boundaries.

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 determine the spectrum completely and allow to derive the Bethe equations for both periodic and general open boundary conditions.