### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Cite this

*Theoretical and Mathematical Physics*,

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

}

*Theoretical and Mathematical Physics*, vol. 136, no. 1, pp. 917-935. https://doi.org/10.1023/A:1024541320960

**Spectral curves and parameterization of a discrete integrable three-dimensional model.** / Pakuliak, SZ; Sergeev, SM.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectral curves and parameterization of a discrete integrable three-dimensional model

AU - Pakuliak, SZ

AU - Sergeev, SM

PY - 2003/7

Y1 - 2003/7

N2 - 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

AB - 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

KW - three-dimensional integrable systems

KW - Backlund transformations

KW - spectral curves

U2 - 10.1023/A:1024541320960

DO - 10.1023/A:1024541320960

M3 - Article

VL - 136

SP - 917

EP - 935

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 1

ER -