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

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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.

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REFERENCES

  1. R. E. Behrend, P. A. Pearce, and D. L. O'Brien, “Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy,” Preprint hep-th/9507118 (1995).

  2. D. L. O'Brien, P. A. Pearce, and S. Ole Warnaar, Physica A, 228, 63 (1996).

    Google Scholar 

  3. F. Alcaraz, M. Barber, and M. Batchelor, Phys. Rev. L ett., 58, 771 (1987); F. Alcaraz, M. Barber, M. Batchelor, R. Baxter, and G. Quispel, J. Phys. A, 20, 6397 (1987).

    Google Scholar 

  4. C. Hamer, J. Phys. A, 14, 2981 (1981).

    Google Scholar 

  5. F. Alcaraz, M. Baake, U. Grimm, and V. Rittenberg, J. Phys. A, 22, L5 (1989).

    Google Scholar 

  6. V. Pasqier and H. Saleur, Nucl. Phys. B, 330, 523 (1990).

    Google Scholar 

  7. A. Belavin and Yu. Stroganov, “Minimal models of integrable lattice theory and truncated functional equations,” Preprint hep-th/9908050 (1999).

  8. E. K. Sklyanin, J. Phys. A, 21, 2375 (1988).

    Google Scholar 

  9. P. P. Kulish and E. K. Sklyanin, J. Phys. A, 24, L435 (1991).

    Google Scholar 

  10. F. C. Alcaraz, A. A. Belavin, and R. A. Usmanov, “Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions,” Preprint hep-th/0007151 (2000).

  11. E. Lusztig, Contemp. Math., 82, 59 (1989).

    Google Scholar 

  12. P. P. Martin, Potts Models and Related Problems in Statistical Mechanics, World Scientific, Singapore (1991).

    Google Scholar 

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Authors and Affiliations

  1. Landau Institute of Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia

    A. A. Belavin & R. A. Usmanov

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  1. A. A. Belavin
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  2. R. A. Usmanov
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Belavin, A.A., Usmanov, R.A. The Minimal LM(3,4) Lattice Model and the Two-Dimensional Ising Model with Cylindrical Boundary Conditions. Theoretical and Mathematical Physics 126, 48–65 (2001). https://doi.org/10.1023/A:1005250030709

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