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arXiv · 1605.02915

Elliptic pfaffians and solvable lattice models

Hjalmar Rosengren
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Abstract

We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.

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Hjalmar Rosengren. 2016-05-10. Elliptic pfaffians and solvable lattice models. https://doi.org/10.1088/1742-5468%2F2016%2F08%2F083106

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