Integrable boundary conditions in the antiferromagnetic Potts model

Abstract

We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $D_2^2$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K-matrices of the $D_2^2$ model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works (arXiv:nlin/0002050 and arXiv:1707.09260) are discussed.

arXiv comment32 pages; typos corrected

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Cited by in corpus (15)

• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Gibbs measures of Potts model on Cayley trees: a survey and applications
• Lattice regularisation of a non-compact boundary conformal field theory
• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• Integrable boundary conditions for staggered vertex models
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• $OSp(n|2m)$ quantum chains with free boundaries
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models