q colourings of the triangular lattice

Nienhuis (1982,4) has shown that the critical O(n) model, on the honeycomb lattice is equivalent to a zero-temperature antiferromagnetic Potts model on the triangular lattice, i.e. to the chromatic polynomial of the triangular lattice. Here the critical O(n) model is solved by the Bethe ansatz method, thereby giving the large-lattice limit of the chromatic polynomial.

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