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 “τ2 (t q )” model. Here we generalize this to obtain a column-inhomogeneous τ2 (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 Nth 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.
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Baxter, R.J. Transfer Matrix Functional Relations for the Generalized τ2 (t q ) Model. Journal of Statistical Physics 117, 1–25 (2004). https://doi.org/10.1023/B:JOSS.0000044062.64287.b9
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DOI: https://doi.org/10.1023/B:JOSS.0000044062.64287.b9