Exact solution of the Faddeev-Volkov model

Details Exact solution of the Faddeev-Volkov model Exact solution of the Faddeev-Volkov model

2007-06-21

arxiv.org/abs/0706.3077v2

Phys.Lett.A372:1547-1550,2008

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1016/j.physleta.2007.10.053

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.

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