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

This article is cited in 2 scientific papers (total in 2 papers)

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

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Received: 30.06.2000

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
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\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
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\pages 63--83
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\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}
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathscinet  zmath  isi
    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  crossref  mathscinet  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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