Spectral curves and parameterization of a discrete integrable three-dimensional model

SZ Pakuliak, SM Sergeev

Research output: Contribution to journalArticle

3 Citations (Scopus)

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
Original languageEnglish
Pages (from-to)917-935
Number of pages19
JournalTheoretical and Mathematical Physics
Volume136
Issue number1
DOIs
Publication statusPublished - Jul 2003
Externally publishedYes

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Spectral Curve
three dimensional models
parameterization
Parameterization
Algebraic curve
Three-dimensional
curves
Integrable Models
Parameterise
Rational Curves
Spin Models
Theta Functions
Periodic Boundary Conditions
Soliton Solution
Ludwig Boltzmann
General Solution
Model
cubic lattices
Curve
fixing

Cite this

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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",
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Spectral curves and parameterization of a discrete integrable three-dimensional model. / Pakuliak, SZ; Sergeev, SM.

In: Theoretical and Mathematical Physics, Vol. 136, No. 1, 07.2003, p. 917-935.

Research output: Contribution to journalArticle

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AU - Sergeev, SM

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AB - 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

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KW - spectral curves

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