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Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry

Bazhanov, Vladimir; Mangazeev, Vladimir; Sergeev, Sergey

Description

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group Uq (sl2). 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...[Show more]

dc.contributor.authorBazhanov, Vladimir
dc.contributor.authorMangazeev, Vladimir
dc.contributor.authorSergeev, Sergey
dc.date.accessioned2015-12-08T22:21:42Z
dc.identifier.issn0550-3213
dc.identifier.urihttp://hdl.handle.net/1885/32234
dc.description.abstractThe Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group Uq (sl2). 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.
dc.publisherElsevier
dc.sourceNuclear Physics B
dc.titleFaddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume784
dc.date.issued2007
local.identifier.absfor010501 - Algebraic Structures in Mathematical Physics
local.identifier.ariespublicationu4056230xPUB90
local.type.statusPublished Version
local.contributor.affiliationBazhanov, Vladimir, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationMangazeev, Vladimir, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationSergeev, Sergey, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage234
local.bibliographicCitation.lastpage258
local.identifier.doi10.1016/j.nuclphysb.2007.05.013
dc.date.updated2015-12-08T08:37:35Z
local.identifier.scopusID2-s2.0-34548700128
CollectionsANU Research Publications

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