We consider the star-triangle relation and the form of its solutions. We present some simple parametrizations of the weight functions of the three-state chiral Potts model. This model does not have the “difference property”: we discuss the resulting difficulties in attempting to use the corner transfer matrix method for this model.
The Nn(n–1)/2-state R-matrix related to U q( sl (n)) algebra at q2N=1 is presented. Its matrix elements are interpreted as Boltzmann weights of an elementary box of some 2D lattice statistical model and given in terms of [Formula: see text] weights of the "minimal" sl (n) chiral Potts model. The corresponding family of transfer matrices depends on n rapidity variables living on high genus algebraic curves, the latter being defined by n moduli. The Yang-Baxter equation is conjectured to hold.
It has recently been shown that the solvable N-state chiral Potts model is related to a vertex model with N-state spins on vertical edges, two-state spins on horizontal edges. Here we generalize this to a “j-state by N-state” model and establish three sets of functional relations between the various transfer matrices. The significance of the “super-integrable” case of the chiral Potts model is discussed, and results reported for its finite-size corrections at criticality.
Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.
Parallel family trees for transfer matrices in the Potts model