### Abstract

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

Pages (from-to) | 65-96 |

Number of pages | 32 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2012 |

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### Cite this

*Advances in Theoretical and Mathematical Physics*,

*16*(1), 65-96. https://doi.org/10.4310/ATMP.2012.v16.n1.a3

}

*Advances in Theoretical and Mathematical Physics*, vol. 16, no. 1, pp. 65-96. https://doi.org/10.4310/ATMP.2012.v16.n1.a3

**A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations.** / Bazhanov, Vladimir V.; Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations

AU - Bazhanov, Vladimir V.

AU - Sergeev, Sergey

PY - 2012/1

Y1 - 2012/1

N2 - We obtain a new solution of the star-triangle relation with positive Boltzmann weights, which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines an exactly solvable two lattice model of statistical mechanics, which involves continuous spin variables, living on a circle, and contains two temperature-like parameters. If one of the these parameters approaches a root of unity (corresponds to zero temperature), the spin variables freezes into discrete positions, equidistantly spaced on the circle. An absolute orientation of these positions on the circle slowly changes between lattice sites by overall rotations. Allowed configurations of these rotations are described by classical discrete integrable equations, closely related to the famous Q4-equations by Adler, Bobenko and Suris. Fluctuations between degenerate ground states in the vicinity of zero temperature are described by a rather general integrable lattice model with discrete spin variables. In some simple special cases, the latter reduces to the Kashiwara-Miwa and chiral Potts models. © 2012 International Press.

AB - We obtain a new solution of the star-triangle relation with positive Boltzmann weights, which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines an exactly solvable two lattice model of statistical mechanics, which involves continuous spin variables, living on a circle, and contains two temperature-like parameters. If one of the these parameters approaches a root of unity (corresponds to zero temperature), the spin variables freezes into discrete positions, equidistantly spaced on the circle. An absolute orientation of these positions on the circle slowly changes between lattice sites by overall rotations. Allowed configurations of these rotations are described by classical discrete integrable equations, closely related to the famous Q4-equations by Adler, Bobenko and Suris. Fluctuations between degenerate ground states in the vicinity of zero temperature are described by a rather general integrable lattice model with discrete spin variables. In some simple special cases, the latter reduces to the Kashiwara-Miwa and chiral Potts models. © 2012 International Press.

U2 - 10.4310/ATMP.2012.v16.n1.a3

DO - 10.4310/ATMP.2012.v16.n1.a3

M3 - Article

VL - 16

SP - 65

EP - 96

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0753

IS - 1

ER -