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On soluble cases of staggered ice-rule on a square lattice

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Book cover Non-Linear Equations in Classical and Quantum Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 226))

Abstract

We discuss a solubility condition for staggered vertex systems with ice-rule and its impacts on the Ashkin-Teller, Potts and layered Potts models.

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References

  1. L. Onsager, Phys. Rev. 65 (1944) 117.

    Article  Google Scholar 

  2. J. Ashkin & E. Teller, Phys. Rev. 64 (1943) 178.

    Article  Google Scholar 

  3. R.B. Potts, Proc. Camb. Phil. Soc. 48 (1952) 106.

    Google Scholar 

  4. E.H. Lieb, Phys. Rev. 162 (1967) 162.

    Google Scholar 

  5. , Phys. Rev. Lett. 18 (1967) 1046

    Article  Google Scholar 

  6. , Phys. Rev. Lett. 19 (1967) 108.

    Article  Google Scholar 

  7. R.J. Baxter, Ann. Phys. (N.Y.) 70 (1972) 193.

    Article  Google Scholar 

  8. F.Y. Wu and K.Y. Lin, Phys. Rev. B12 (1975) 419.

    Google Scholar 

  9. K.Y. Lin, J. Phys. A8 (1975) 1899.

    Google Scholar 

  10. K.Y. Lin and I.P. Wang, J. Phys. A10 (1977) 813.

    Google Scholar 

  11. R.J. Baxter, Stud. appl. Math. 50 (1971) 51.

    Google Scholar 

  12. R.J. Baxter, Proc. R. Soc. Lond. A383 (1982) 43.

    Google Scholar 

  13. R.Z. Bariev, Theor. Math. Phys. 49 (1982) 1021.

    Article  Google Scholar 

  14. E.H. Lieb and F.Y. Wu, in “Phase Transitions and Critical Phenomena” (C. Domb and M.S. Green, eds.) Vol. 1 (1972) pp. 321–490. Academic Press, London.

    Google Scholar 

  15. R.J. Baxter, Jour. Stat. Phys. 22 (1982) 1.

    Article  Google Scholar 

  16. L.A. Takhtadzhan and L.D. Faddeev, Russ. Math. Surveys 34 (1979) 11.

    Google Scholar 

  17. A.B. Zamolodchikov and Al.B. Zamolodchikov, Nucl. Phys. B133 (1978) 525.

    Article  Google Scholar 

  18. M. Karowski, H.J. Thun, T.T. Truong and P.H. Weisz, Phys. Lett. 67B (1977) 321.

    Google Scholar 

  19. R.J. Baxter, Phil. Trans. Roy. Soc. (London) 289 (1978) 315.

    Google Scholar 

  20. T.T. Truong and K.D. Schotte, Nucl. Phys. B220 (FS 8) (1983) 77.

    Article  Google Scholar 

  21. T.T. Truong, Physica 122A (1984) 603.

    MathSciNet  Google Scholar 

  22. H.N.V. Temperley and E.H. Lieb, Proc. Roy. Soc. (London) A322 (1971) 251.

    Google Scholar 

  23. R.J. Baxter, S.B. Kelland and F.Y. Wu, J. Phys. A9 (1976) 397.

    Google Scholar 

  24. M.T. Jaeckel and J.M. Maillard, J. Phys. A15 (1982) 2241.

    Google Scholar 

  25. T.T. Truong, J. Phys. A17 (1984) L473.

    Google Scholar 

  26. C. Fan, Phys. Lett. 39A (1972) 136.

    Google Scholar 

  27. F.J. Wegner, J. Phys. C5 (1972) L131.

    Google Scholar 

  28. M. Kohmoto, M. den Nijs and L.P. Kadanoff, Phys. Rev. B24 (1981) 5229.

    Google Scholar 

  29. R.V. Ditzian, J.R. Banavar, G.S. Grest and L.P. Kadanoff, Phys. Rev. B22 (1980) 2542.

    Google Scholar 

  30. A. Luther, Phys. Rev. B14 (1976) 2153.

    Google Scholar 

  31. M. Lüscher, Nucl. Phys. B117 (1976) 475.

    Article  Google Scholar 

  32. T.T. Truong and K.D. Schotte, Nucl. Phys. B230 (FS 10) (1984) 1.

    Article  Google Scholar 

  33. R. Shankar, Phys. Lett. B102 (1981) 257.

    Google Scholar 

  34. I. Peschel and F. Rys, Phys. Lett. 91A (1982) 187.

    Google Scholar 

  35. M. Barber and F. Rys, “The critical lines of an asymmetric 8-vertex model”. Preprint 1984. Australian National University.

    Google Scholar 

  36. I.V. Cherednik, Theor. Math. Phys. 43 (1980) 117, 356.

    Article  Google Scholar 

  37. C.L. Schultz, Phys. Rev. Lett. 46 (181) 629.

    Article  Google Scholar 

  38. D. Babelon, H.J. de Vega and C.M. Viallet, Nucl. Phys. B150 (FS 8) (1981) 542.

    Article  Google Scholar 

  39. G.E. Andrews, R.J. Baxter and P.J. Forrester, Jour. Stat. Phys. ul35 (1984) 193.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-1000, Berlin 33, W. Germany

    T. T. Truong

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  1. T. T. Truong
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N. Sanchez

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© 1985 Springer-Verlag

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Truong, T.T. (1985). On soluble cases of staggered ice-rule on a square lattice. In: Sanchez, N. (eds) Non-Linear Equations in Classical and Quantum Field Theory. Lecture Notes in Physics, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15213-X_81

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  • DOI: https://doi.org/10.1007/3-540-15213-X_81

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15213-2

  • Online ISBN: 978-3-540-39352-8

  • eBook Packages: Springer Book Archive

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