Boundary \(K\)-matrices for the six vertex and the \(n(2n-1)A_{n-1}\) vertex models. (English) Zbl 0786.58020
Summary: Boundary conditions compatible with integrability are obtained for two- dimensional models by solving the factorizability equations for the reflection matrices \(K^ \pm(\theta)\). For the six vertex model the general solution depending on four arbitrary parameters is found. For the \(A_{n-1}\) models all diagonal solutions are found. The associated integrable magnetic Hamiltonians are explicitly derived.
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 81T25 | Quantum field theory on lattices |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
