where ∗ ∗ denotes complex conjugation and the x k ( r r ′ ) are related to the interaction strength along the edge r r ′ . Note that x k ( r r ′ ) = x N − − k ( r r ′ ) and x 0 are often set to 1. The (real valued) Boltzmann weights are invariant under the transformations s r → → ω ω k s r and s r → → s r ∗ ∗ , analogous to universal rotation and reflection respectively.