R. J. Baxter

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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(tq)” model. Here we generalize this to obtain a column-inhomogeneous τ2(tq) model, and derive the functional relations satisfied by its row-to-row transfer matrix. We do not need the usual chiral Potts(More)
An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the(More)
We adapt our previous results for the “partition function” of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e−αH , where H is the associated hamiltonian. The spontaneous magnetization Mr can be expressed in terms of particular matrix elements of e−αHSr 1e −βH , where S1 is a diagonal matrix. We(More)
This is the third in a series of papers in which we set up and discuss the functional relations for the “split rapidity line” correlation function in the N–state chiral Potts model. The order parameters of the model can be obtained from this function. Here we consider the case N = 3 and write the equations explicitly in terms of the hyperelliptic functions(More)
As a by-product of a finite-size Bethe ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like 1− q √ n and 1− qn2, instead of 1− qn. We show here that there is(More)