## Abstract

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.

Original language | English |
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Pages (from-to) | 234-258 |

Number of pages | 25 |

Journal | Nuclear Physics B |

Volume | 784 |

Issue number | 3 |

DOIs | |

Publication status | Published - 19 Nov 2007 |