### Abstract

We consider the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model with elliptic weights, the SOS model. We provide explicit solutions as theta functions. On the so-called combinatorial line, in which the model is equivalent to the three-colour model, these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions.

Original language | English |
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Article number | 064001 |

Number of pages | 26 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 6 |

DOIs | |

Publication status | Published - 12 Feb 2016 |

### Keywords

- quantum Knizhnik-Zamolodchikov equation
- SOS model
- three-colour model
- FREE-FIELD CONSTRUCTION
- ZUMINO-WITTEN MODELS
- 8-VERTEX MODEL
- POLYNOMIAL SOLUTIONS
- BETHE-ANSATZ
- SPIN CHAINS
- SOS MODEL
- XXZ CHAIN
- LATTICE
- COMBINATORICS

## Profiles

## Robert Andrew Weston

- School of Mathematical & Computer Sciences, Mathematics - Professor
- School of Mathematical & Computer Sciences - Professor

Person: Academic (Research & Teaching)

## Cite this

Finch, P. E., Weston, R. A., & Zinn-Justin, P. (2016). Theta function solutions of the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model.

*Journal of Physics A: Mathematical and Theoretical*,*49*(6), [064001]. https://doi.org/10.1088/1751-8113/49/6/064001