Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

Details Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

2007-03-05

arxiv.org/abs/hep-th/0703041v2

Nucl.Phys.B784:234-258,2007

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 18 color figures, minor corrections

Scientific paper

10.1016/j.nuclphysb.2007.05.013

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 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.

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