Faddeev-Volkov solution of the Yang- Baxter equation and discrete conformal symmetry

Bazhanov Vladimir, Vladimir Mangazeev, Sergey Sergeev

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)


The Faddeev–Volkov solution of the star-triangle relation is connected with the modular double of the quantum group Uq(sl2). It defines an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. The free energy of the model is exactly calculated in the thermodynamic limit. The model describes quantum fluctuations of circle patterns and the associated discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In particular, in the quasi-classical limit the model precisely describe the geometry of integrable circle patterns with prescribed intersection angles
Original languageEnglish
Pages (from-to)234-258
Number of pages25
JournalNuclear Physics B
Issue number3
Publication statusPublished - 19 Nov 2007
Externally publishedYes


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