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Prog. Theor. Phys. Vol. 52 No. 3 (1974) pp. 871-885

[ Full Text PDF : FREE ACCESS (1036K) ]

Critical Relaxation of a Non-Linear Fokker-Planck Equation

Hideo Yahata

Department of Materials Science, Faculty of Science, Hiroshima University, Hiroshima

(Received March 13, 1974)

Abstract:

The Fokker-Planck equation whose equilibrium solution is given by Wilson's probability density is considered. The conditional probability of the temporal process generated through this equation is expressed in the form of a path integral. With the aid of renormalization group transformations applied to this path probability density, the dynamical critical exponent characterizing asymptotic critical behavior of its long wavelength mode is determined to order ε2 (ε= 4-d) in agreement with that of Halperin, Hohenberg and Ma.


URL : http://ptp.ipap.jp/link?PTP/52/871/
DOI : 10.1143/PTP.52.871

[ Full Text PDF : FREE ACCESS (1036K) ] Citation:

References:

  1. B. I. Halperin, P. C. Hohenberg and S. Ma, Phys. Rev. Lett. 29 (1972), 1548[APS].
  2. K. G. Wilson and J. Kogut, The Renormalization Group and the ε Expansion (1972).
  3. K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28 (1972), 240[APS].
  4. K. G. Wilson, Phys. Rev. Lett. 28 (1972), 548[APS].
  5. M. Suzuki and G. Igarashi, Prog. Theor. Phys. 49 (1973), 1070[PTP].
  6. M. Suzuki, Prog. Theor. Phys. 50 (1973), 1767[PTP]; ibid. 51 (1974), 1257[PTP].
  7. G. Igarashi, preprint.
  8. Y. Kuramoto, Prog. Theor. Phys. 51 (1974), 1712[PTP].
  9. K. G. Wilson, Phys. Rev. B 4 (1971), 3174[APS]; ibid. 4 (1971), 3184[APS].
  10. N. Hashitsume, Prog. Theor. Phys. 8 (1952), 461[PTP]; ibid. 15 (1956), 369[PTP].
  11. L. Onsager and S. Machlup, Phys. Rev. 91 (1953), 1505[APS].
  12. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
  13. R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973), 51[CrossRef].
  14. R. Graham, Springer Tracts in Modern Physics, 66 (Springer 1973), p. 1.
  15. H. Yahata and M. Suzuki, J. Phys. Soc. Jpn. 27 (1969), 1421[JPSJ].
    H. Yahata, J. Phys. Soc. Jpn. 30 (1971), 657[JPSJ].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 53 No. 1 (1975) pp. 97-110 :
    On the Critical Dynamics in Bose Systems and the Time-Dependent Ginzburg-Landau Model
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 54 No. 6 (1975) pp. 1679-1692 :
    Coherent Representation of Dynamical Renormalization Group in Bose Systems
    Fumihiko Tanaka
  3. Progress of Theoretical Physics Vol. 61 No. 3 (1979) pp. 864-880 :
    Real-Space Renormalization Group Approach to Critical Dynamics
    Masuo Suzuki, Kiyoshi Sogo, Ikuo Matsuba, Hiroshi Ikeda, Terumi Chikama and Hiroshi Takano

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