Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-03-05
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.
Bazhanov Vladimir V.
Mangazeev Vladimir V.
Sergeev Sergey M.
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