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- George E. Andrews, R. J. Baxter, David M. Bressoud, William H. Burge, P. J. Forrester, Gérard Viennot
- Eur. J. Comb.
- 1987

- R J Baxter
- 2004

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)

- R J Baxter
- 2008

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)

- R. J. Baxter
- 2008

We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the q-state Potts model randomized over such maps. Like the regular ferromagnetic lattice models, it has a… (More)

- R J Baxter
- 2008

We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the “beyond the equator”, infinite momenta and exact complete string problems. We show how they can be overcome and conclude that the coordinate… (More)

- R. J. Baxter
- 1988

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)

- R. J. Baxter
- 1998

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)

- R J Baxter
- Physical review letters
- 2005

We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.

- V V Bazhanov, R J Baxter
- 1992

The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with twoand threespin interactions. The corresponding local Boltzmann weights obey a number of simple relations,… (More)

- R J Baxter
- 1998

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)