### Abstract

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

Pages (from-to) | 310-321 |

Number of pages | 12 |

Journal | Theoretical and Mathematical Physics |

Volume | 138 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2004 |

Externally published | Yes |

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### Cite this

*Theoretical and Mathematical Physics*,

*138*(3), 310-321. https://doi.org/10.1023/B:TAMP.0000018448.40360.3d

}

*Theoretical and Mathematical Physics*, vol. 138, no. 3, pp. 310-321. https://doi.org/10.1023/B:TAMP.0000018448.40360.3d

**Evidence for a phase transition in three-dimensional lattice models.** / Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Evidence for a phase transition in three-dimensional lattice models

AU - Sergeev, Sergey

PY - 2004/3

Y1 - 2004/3

N2 - It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a “chess spin lattice” related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case

AB - It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a “chess spin lattice” related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case

KW - three-dimensional integrable models

KW - Zamolodchikov-Bazhanov-Baxter model

U2 - 10.1023/B:TAMP.0000018448.40360.3d

DO - 10.1023/B:TAMP.0000018448.40360.3d

M3 - Article

VL - 138

SP - 310

EP - 321

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 3

ER -