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 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.

4 pages

References in corpus (4)

• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Abelian Current Algebra and the Virasoro Algebra on the Lattice
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

Cited by in corpus (33)

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• Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
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• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Elliptic beta integrals and solvable models of statistical mechanics
• On Complex Gamma-Function Integrals
• The Endless Beta Integrals
• Barnes-Ismagilov integrals and hypergeometric functions of the complex field
• Integrable quad equations derived from the quantum Yang-Baxter equation
• Complex hypergeometric functions and integrable many-body problems
• Integrable lattice spin models from supersymmetric dualities
• $\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals
• From rarefied elliptic beta integral to parafermionic star-triangle relation
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• The Yang-Baxter relation and gauge invariance
• Gustafson integrals for $SL(2,\mathbb{C})$ spin magnet
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• Lens partition function, pentagon identity and star-triangle relation
• The rarefied elliptic Bailey lemma and the Yang-Baxter equation
• Exactly solved models on planar graphs with vertices in ${\mathbb{Z}}^3$
• On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models
• General modular quantum dilogarithm and beta integrals
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group
• New Pentagon Identities Revisited
• Chiral Potts model and the discrete Sine-Gordon model at roots of unity
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Complex rational Ruijsenaars model. The two-particle case
• Complex and rational hypergeometric functions on root systems
• Regge symmetry of 6j-symbols of the Lorentz group