Exact solution of the Faddeev-Volkov model

Abstract

The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group Uq (sl2). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c → + ∞ the model describes quantum fluctuations of discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In the strongly-coupled limit c → 1 the model turns into a discrete version of the D = 2 Zamolodchikov's "fishing-net" model.