Elliptic pfaffians and solvable lattice models

@article{Rosengren2016EllipticPA,
  title={Elliptic pfaffians and solvable lattice models},
  author={Hjalmar Rosengren},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2016},
  volume={2016}
}
  • H. Rosengren
  • Published 10 May 2016
  • Mathematics
  • Journal of Statistical Mechanics: Theory and Experiment
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… 

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