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The Migdal approximation and other new methods in the real-space renormalization group approach to critical dynamics

  • Masuo Suzuki
Real Space Dynamical Renomalization Group Methods
Part of the Lecture Notes in Physics book series (LNP, volume 104)

Abstract

A historical review o£ linear and nonlinear critical slowing down is briefly given for the kinetic Ising model. Several recent papers on the real-space RG approach to critical dynamics are also reviewed briefly. The main part of this paper is to present the fundamental idea of the real-space RG approach and to explain explicitly the Migdal approach to critical dynamics.

Keywords

Critical Exponent Coarse Graining Potential Moving Critical Dynamic Path Integral Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R.J. Glauber, J. math. Phys. 4 (1963) 294.CrossRefGoogle Scholar
  2. 2.
    M. Suzuki and R. Kubo, J. Phys. Soc. Japan 24 (1968) 51.Google Scholar
  3. 3.
    M. Suzuki, Prog. Theor. Phys. 43 (1970) 882Google Scholar
  4. 4.
    R. Kubo, J. Phys. Soc. Japan 12 (1957) 570.Google Scholar
  5. 5.
    M. Suzuki, H. Ikari (Yahata) and R. Kubo, J. Phys. Soc. Japan 26 (1969) supplement, 153.Google Scholar
  6. 6.
    H. Yahata and M. Suzuki, J. Phys. Soc. Japan 27 (1969) 1421.Google Scholar
  7. 7.
    M. Suzuki, Int. J. Magnetism, 1 (1971) 123.Google Scholar
  8. 8.
    M. Suzuki, in Critical Phenomena in Alloy Magnets, and Superconductors (ed. R.E. Mills, E. Ascher and R.I. Jaffee; 1971) Mcgraw-Hill Book Co., New York.Google Scholar
  9. 9.
    Z. Rácz, Phys. Lett. 53A (1975) 433.Google Scholar
  10. 10.
    Z. Rácz, Phys. Rev. B13 (1976) 263.Google Scholar
  11. 11.
    M.E. Fisher and Z. Rácz, Phys. B13 (1976) 5039.Google Scholar
  12. 12.
    Z. Rácz, ref. 10. B13 (1976) 263.Google Scholar
  13. 13.
    Z. Csépes and Z. Rácz, J. Phys. A: Math. Gen. Vol. 11 (1978) No.3, 575.CrossRefGoogle Scholar
  14. 14.
    R. Bausch and H.K. Janssen, Z. Phys. B25 (1976) 275.Google Scholar
  15. 14a.
    K. Binder, Phys. Rev. B8 (1973) 3423.Google Scholar
  16. 15.
    M. Suzuki, Phys. Lett. 58A (1976) 435.Google Scholar
  17. 16.
    Z. Rácz and M.F. Collinz, Phys. Rev. B13 (1976) 3074.Google Scholar
  18. 17.
    H. Ikeda, Prog. Theor. Phys. 55 (1976) 2027; ibid 57 (1977) 687.Google Scholar
  19. 18.
    N.J. White, J. Phys. C: Solid St. Phys. 9 (1976) L187.CrossRefGoogle Scholar
  20. 19.
    M. Suzuki and H. Ikeda, Prog. Theor. Phys. 55 (1976) 2041.Google Scholar
  21. 20.
    R. Kretschmer, K. Binder and D. Stauffer, J Stat. Phys. 15 (1976) 267.CrossRefGoogle Scholar
  22. 21.
    A. Rácz and T. Tél, Phys. Lett. 60A (1977) 3.Google Scholar
  23. 22.
    L.P. Kadanoff, Physics 2 (1966) 263.Google Scholar
  24. 23.
    M. Suzuki, Prog. Theor. Phys. 51 (1974) 1257.Google Scholar
  25. 24.
    H. Mori, Prog. Theor. Phys. 52 (1974) 433; 53 (1975) 1617; 57 (1977) 785.Google Scholar
  26. 25.
    M. Suzuki, Prog. Theor. Phys. 56 (1976) 77; 56 (1976) 477; 57 (1977) 380; J. Stat. Phys. 16 (1977) 11; 16 (1977) 477.Google Scholar
  27. 26.
    M. Suzuki, K. Sogo, I. Mastuba, H. Ikeda, T. Chikama and H. Takano, Prog. Theor. Phys. 61 (1979) No.3.Google Scholar
  28. 27.
    K.G. Wilson, Phys. Rev. B4 (1971), 3174, 3184.Google Scholar
  29. 28.
    K.G. Wilson and J. Kogut, Phys. Rep. C12 (1974) 75; M.E. Fisher, Rev. Mod. Phys. 46 (1974) 597.CrossRefGoogle Scholar
  30. 29.
    S. Ma, Phys. Rev Lett. 37 (1976) 461.CrossRefGoogle Scholar
  31. 30.
    W. Kinzel, Z. Phys. B29 (1978) 361.Google Scholar
  32. 31.
    Y. Achiam, J. Phys. A11 (1978) 975.Google Scholar
  33. 32.
    Y. Achiam, J. Phys. A11 (1978) L129; preprint.Google Scholar
  34. 33.
    Y. Achiam and J.M. Kosterlitz, Phys. Rev. Lett. 41 (1978) 128.Google Scholar
  35. 34.
    G.F. Mazenko, M.J. Nolan and O.T. Valls, Phys. Rev. Lett. 41 (1978) 500.CrossRefGoogle Scholar
  36. 35.
    M. Suzuki et al. ref. 26.Google Scholar
  37. 36.
    S.T. Chui, G. Forgacs and H.L. Frisch, preprint.Google Scholar
  38. 37.
    U. Deker, Z. Phys. B31 (1978) 283.Google Scholar
  39. 38.
    Y. Shiwa, preprint.Google Scholar
  40. 39.
    R. Abe, Prog. Theor. Phys. 39 (1968) 947.Google Scholar
  41. 40.
    B.U. Felderhof, Reports on math. Phys. 1 (1970) 215.Google Scholar
  42. 41.
    B.U. Felderhof and M. Suzuki, Physics 56 (1971) 43.Google Scholar
  43. 42.
    H.J. Hilhorst, M. Suzuki and B.U. Felderhof, Physica 60 (1972) 199.Google Scholar
  44. 43.
    M. Suzuki, Phys. Lett. 19 (1965) 267.Google Scholar
  45. 44.
    D.R. Nelson and M.E. Fisher, Ann. Phys. (N.Y.) 91 (1975) 266.Google Scholar
  46. 44a.
    R.G. Priest, Phys. Rev. B11 (1975) 3461.Google Scholar
  47. 45.
    A.A. Migdal, Zh. Eksp. Teor. Fiz. 69 (1975) 1457; ibid. 69 (1975) 810.Google Scholar
  48. 46.
    L.P. Kadanoff, Ann. Phys. (N.Y.) 100 (1976) 359.Google Scholar
  49. 47.
    The present author has received a letter to our critical comments to the first version of Chui et al.Google Scholar
  50. 48.
    Th. Niemeijer and J.M.J. van Leeuwen, Phys. Rev. Lett. 31 (1973) 1411; Physica 71A (1974) 17.CrossRefGoogle Scholar
  51. 49.
    S. Ma, preprint.Google Scholar
  52. 50.
    M. Suzuki, unpublished.Google Scholar
  53. 51.
    R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973) 51.Google Scholar
  54. 52.
    H.K. Janssen, Z. Phys. B23 (1976) 377.Google Scholar
  55. 53.
    F. Langouche, D. Roekaerts and E. Tirapequi, preprints.Google Scholar
  56. 54.
    C.P. Enz, Lecture Notes in Physics, Vol. 54, p.79, Springer.Google Scholar
  57. 55.
    M. Suzuki, Phys. Lett. 67A (1978) 339; Prog. Theor. Phys. 64 (1978) supplement; in Synergetics: Far from EquiZibrium, ed. A. Pacault and C. Vidal, Springer-Verlag 1979; Proceedings of the 17th Inter national Solvay Conference, November 1968, in press.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Masuo Suzuki
    • 1
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan

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