# 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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The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a 2 + ab)(b 2 + ab) = (c 2 + ab)(d 2 + ab) is considered. Its transfer matrix with L = 2n + 1, n ⩾ 0,
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In this work, we study an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group Ep,γ[gl2^] as its underlying symmetry algebra. We elaborate on results previously
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