Transfer matrix functional relations for the generalized τ 2 ( t q ) model

Transfer matrix functional relations for the generalized τ 2 (t q) model Abstract The N-state chiral Potts model in lattice statistical mechanics can be obtained as a " descendant " of the six-vertex model, via an intermediate " Q " or " τ 2 (t q) " model. Here we generalize this to obtain a column-inhomogeneous τ 2 (t q) model, and derive the functional relations satisfied by its row-to-row transfer matrix. We do not need the usual chiral Potts relations between the N th powers of the rapidity parameters a p , b p , c p , d p of each column. This enables us to readily consider the case of fixed-spin boundary conditions on the left and right-most columns. We thereby re-derive the simple direct product structure of the transfer matrix eigenvalues of this model, which is closely related to the superintegrable chiral Potts model with fixed-spin boundary conditions.