Exact solution of the Faddeev-Volkov model

TL;DR

This paper provides an exact solution for the Faddeev-Volkov model, a lattice model related to quantum groups and conformal transformations, calculating its free energy and exploring various limits.

Contribution

It presents the exact calculation of the free energy of the Faddeev-Volkov model in the thermodynamic limit, linking it to quantum and classical conformal theories.

Findings

Exact free energy in the thermodynamic limit

Connection to quantum fluctuations of conformal transformations

Behavior in classical and strongly-coupled limits

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 U_q(sl_2). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c->infinity 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.