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

S. Z. Pakuliak*, S. M. Sergeev

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    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(Russian Federation)
    Volume136
    Issue number1
    DOIs
    Publication statusPublished - Jul 2003

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