### Abstract

We consider a discrete classical integrable model on a three-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of various three-dimensional spin models. We find the general solution of this model constructed in terms of the theta functions defined on an arbitrary compact algebraic curve. Imposing periodic boundary conditions fixes the algebraic curve. We show that the curve then coincides with the spectral curve of the auxiliary linear problem. For a rational curve, we construct the soliton solution of the model

Original language | English |
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Pages (from-to) | 917-935 |

Number of pages | 19 |

Journal | Theoretical and Mathematical Physics |

Volume | 136 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2003 |

Externally published | Yes |

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## Cite this

Pakuliak, SZ., & Sergeev, SM. (2003). Spectral curves and parameterization of a discrete integrable three-dimensional model.

*Theoretical and Mathematical Physics*,*136*(1), 917-935. https://doi.org/10.1023/A:1024541320960