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- W3103119507 abstract "In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of freedom at each site of the lattice. The Yang-Baxter equation for such models takes a particular simple form called the star-triangle relation. Interestigly all known solutions of this relation can be obtained as particular cases of a single master solution, which is expressed through the elliptic gamma function and have continuous spins taking values of the circle. We show that in the low-temperature (or quasi-classical) limit these lattice models reproduce classical discrete integrable systems on planar graphs previously obtained and classified by Adler, Bobenko and Suris through the consistency-around-a-cube approach. We also discuss inversion relations, the physicical meaning of Baxter's rapidity-independent parameter in the star-triangle relations and the invariance of the action of the classical systems under the star-triangle (or cube-flip) transformation of the lattice, which is a direct consequence of Baxter's Z-invariance in the associated lattice models." @default.
- W3103119507 created "2020-11-23" @default.
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- W3103119507 date "2016-10-21" @default.
- W3103119507 modified "2023-10-16" @default.
- W3103119507 title "Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs" @default.
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- W3103119507 doi "https://doi.org/10.1088/1751-8113/49/46/464001" @default.
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