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

Vladimir V. Bazhanov, Vladimir V. Mangazeev, Sergey M. Sergeev
2007 Nuclear Physics B  
The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). 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
more » ... ogue 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.
doi:10.1016/j.nuclphysb.2007.05.013 fatcat:ipyu22hqxrb4rkuitmgfbbfvti