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 TMF, 2001, Volume 126, Number 1, Pages 63–83 (Mi tmf415)

The Minimal $LM(3,4)$ Lattice Model and the Two-Dimensional Ising Model with Cylindrical Boundary Conditions

A. A. Belavin, R. A. Usmanov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We consider an integrable $XXZ$ model with some special open boundary conditions and one-dimensional Ising quantum chains with four different boundary conditions. We show that each of the Ising chains coincides with the minimal $LM(3,4)$ lattice model resulting from the quantum group reduction of the $XXZ$ model and the number of nodes in the former model is determined by the type of boundary conditions. The relation between the two-dimensional Ising model with four different types of boundary conditions and the $LM(3,4)$ model is established.

DOI: https://doi.org/10.4213/tmf415

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English version:
Theoretical and Mathematical Physics, 2001, 126:1, 48–65

Bibliographic databases:

Citation: A. A. Belavin, R. A. Usmanov, “The Minimal $LM(3,4)$ Lattice Model and the Two-Dimensional Ising Model with Cylindrical Boundary Conditions”, TMF, 126:1 (2001), 63–83; Theoret. and Math. Phys., 126:1 (2001), 48–65

Citation in format AMSBIB
\Bibitem{BelUsm01} \by A.~A.~Belavin, R.~A.~Usmanov \paper The Minimal $LM(3,4)$ Lattice Model and the Two-Dimensional Ising Model with Cylindrical Boundary Conditions \jour TMF \yr 2001 \vol 126 \issue 1 \pages 63--83 \mathnet{http://mi.mathnet.ru/tmf415} \crossref{https://doi.org/10.4213/tmf415} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1858196} \zmath{https://zbmath.org/?q=an:1018.82003} \transl \jour Theoret. and Math. Phys. \yr 2001 \vol 126 \issue 1 \pages 48--65 \crossref{https://doi.org/10.1023/A:1005250030709} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000168642200002} 

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• http://mi.mathnet.ru/eng/tmf/v126/i1/p63

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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. Usmanov R.A., “Correspondence between the XXZ model in roots of unity and the one-dimensional quantum ising chain with different boundary conditions”, Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 35, 2001, 321–331
2. Nichols, A, “The Temperley-Lieb algebra and its generalizations in the Potts and XXZ models”, Journal of Statistical Mechanics-Theory and Experiment, 2006, P01003
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