Spectral Curves and Parameterization of a Discrete Integrable Three-dimensional Model
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We consider a discrete classical integrable model on a three-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of various three-dimensional spin models. We find the general solution of this model constructed in terms of the theta functions defined on an arbitrary compact algebraic curve. Imposing periodic boundary conditions fixes the algebraic curve. We show that the curve then coincides with the spectral curve of the auxiliary linear...[Show more]
dc.contributor.author | Pakuliak, S | |
---|---|---|
dc.contributor.author | Sergeev, Sergey | |
dc.date.accessioned | 2015-12-13T23:12:00Z | |
dc.identifier.issn | 0040-5779 | |
dc.identifier.uri | http://hdl.handle.net/1885/87848 | |
dc.description.abstract | We consider a discrete classical integrable model on a three-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of various three-dimensional spin models. We find the general solution of this model constructed in terms of the theta functions defined on an arbitrary compact algebraic curve. Imposing periodic boundary conditions fixes the algebraic curve. We show that the curve then coincides with the spectral curve of the auxiliary linear problem. For a rational curve, we construct the soliton solution of the model. | |
dc.publisher | Plenum Publishing Corporation | |
dc.source | Theoretical and Mathematical Physics | |
dc.subject | Keywords: Bäcklund transformations; Spectral curves; Three-dimensional integrable systems | |
dc.title | Spectral Curves and Parameterization of a Discrete Integrable Three-dimensional Model | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
local.identifier.citationvolume | 136 | |
dc.date.issued | 2003 | |
local.identifier.absfor | 010501 - Algebraic Structures in Mathematical Physics | |
local.identifier.ariespublication | MigratedxPub17313 | |
local.type.status | Published Version | |
local.contributor.affiliation | Pakuliak, S, Joint Institute for Nuclear Research, Moscow | |
local.contributor.affiliation | Sergeev, Sergey, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 1 | |
local.bibliographicCitation.startpage | 917 | |
local.bibliographicCitation.lastpage | 935 | |
local.identifier.doi | 10.1023/A:1024541320960 | |
dc.date.updated | 2015-12-12T08:29:59Z | |
local.identifier.scopusID | 2-s2.0-0037489788 | |
Collections | ANU Research Publications |
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