### Abstract

In this paper we construct a three-dimensional (3D) solvable lattice model with
non-negative Boltzmann weights. The spin variables in the model are assigned
to edges of the 3D cubic lattice and run over an infinite number of discrete
states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D
generalization of the Yang–Baxter equation. The weights depend on a free
parameter 0 < q < 1 and three continuous field variables. The layer-to-layer
transfer matrices of the model form a two-parameter commutative family. This
is the first example of a non-trivial solvable 3D lattice model with non-negative
Boltzmann weights.

Original language | English |
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Pages (from-to) | 1-16 |

Number of pages | 16 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 46 |

DOIs | |

Publication status | Published - 22 Nov 2013 |

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## Cite this

Mangazeev, V. V., Bazhanov, V. V., & Sergeev, S. (2013). An integrable 3D lattice model with positive Boltzmann weights.

*Journal of Physics A: Mathematical and Theoretical*,*46*(46), 1-16. https://doi.org/10.1088/1751-8113/46/46/465206