RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2003, Volume 136, Number 1, Pages 30–51 (Mi tmf214)  

This article is cited in 3 scientific papers (total in 3 papers)

Spectral Curves and Parameterization of a Discrete Integrable Three-Dimensional Model

S. Z. Pakulyaka, S. M. Sergeevb

a Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
b Australian National University

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.

Keywords: three-dimensional integrable systems, Bäcklund transformations, spectral curves

DOI: https://doi.org/10.4213/tmf214

Full text: PDF file (339 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2003, 136:1, 917–935

Bibliographic databases:

Received: 23.08.2002

Citation: S. Z. Pakulyak, S. M. Sergeev, “Spectral Curves and Parameterization of a Discrete Integrable Three-Dimensional Model”, TMF, 136:1 (2003), 30–51; Theoret. and Math. Phys., 136:1 (2003), 917–935

Citation in format AMSBIB
\Bibitem{PakSer03}
\by S.~Z.~Pakulyak, S.~M.~Sergeev
\paper Spectral Curves and Parameterization of a Discrete Integrable Three-Dimensional Model
\jour TMF
\yr 2003
\vol 136
\issue 1
\pages 30--51
\mathnet{http://mi.mathnet.ru/tmf214}
\crossref{https://doi.org/10.4213/tmf214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2025782}
\elib{http://elibrary.ru/item.asp?id=13436753}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 136
\issue 1
\pages 917--935
\crossref{https://doi.org/10.1023/A:1024541320960}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184767700003}


Linking options:
  • http://mi.mathnet.ru/eng/tmf214
  • https://doi.org/10.4213/tmf214
  • http://mi.mathnet.ru/eng/tmf/v136/i1/p30

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Sergeev, “Evidence for a Phase Transition in Three-Dimensional Lattice Models”, Theoret. and Math. Phys., 138:3 (2004), 310–321  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. von Gehlen G, Pakuliak S, Sergeev S, “The Bazhanov-Stroganov model from 3D approach”, Journal of Physics A-Mathematical and General, 38:33 (2005), 7269–7298  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. Von Gehlen G., Pakuliak S., Sergeev S., “3-dimensional integrable lattice models and the Bazhanov-Stroganov model”, Differential Geometry and Physics, Nankai Tracts in Mathematics, 10, 2006, 210–220  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:251
    Full text:81
    References:35
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019