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Prog. Theor. Phys. Vol. 58 No. 4 (1977) pp. 1142-1150

[ Full Text PDF : FREE ACCESS (590K) ]

Static and Dynamic Finite-Size Scaling Theory Based on the Renormalization Group Approach

Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo 113

(Received March 22, 1977)

Abstract:

Fisher's static finite-size scaling law is derived on the basis of the renormalization group theory and it is extended to dynamic critical phenomena in a finite system. This dynamic finite-size scaling law yields a cross-over effect with respect to the size and time-region. This effect is useful in analyzing computer simulations and also in studying the scaling property of the Kondo effect near the absolute zero temperature.


URL : http://ptp.ipap.jp/link?PTP/58/1142/
DOI : 10.1143/PTP.58.1142

[ Full Text PDF : FREE ACCESS (590K) ] Citation:

References:

  1. M. E. Fisher, in Critical Phenomena, edited by M. S. Green, Proc. 51st Enrico Fermi Summer School, Varena, Italy (Academic, New York, 1971).
    M. E. Fisher, J. Vac. Sci. and Tech. 10 (1973), 665.
    M. E. Fisher and M. N. Barbar, Phys. Rev. Lett. 28 (1972), 1516[APS].
  2. K. Binder and D. P. Landau, Phys. Rev. B 13 (1976), 1140[APS].
  3. D. P. Landau, Phys. Rev. B 14 (1976), 263[APS].
  4. M. Suzuki, Prog. Theor. Phys. 58 (1977), 755[PTP].
  5. M. Suzuki, Prog. Theor. Phys. 56 (1976), 1454[PTP].
  6. M. Suzuki, Commun. Math. Phys. 51 (1976), 183, [CrossRef]and references cited therein.
  7. M. Suzuki, reported at Banff Summer School on Critical Phenomena, September 2, 1976.
  8. K. G. Wilson and J. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
  9. M. E. Fisher, Rev. Mod. Phys. 46 (1974), 597[APS].
  10. M. Suzuki, Phys. Lett. A 58 (1976), 435[CrossRef].
    See also the following papers concerning the generating function or time-dependent free energy in non-equilibrium systems: M. Suzuki, Prog. Theor. Phys. 53 (1975), 1657[PTP]; J. Stat. Phys. 14 (1976), 129.
  11. J. Hubbard, Phys. Lett. A 40 (1972), 111[CrossRef].
  12. E. Riedel and F. Wegner, Z. Phys. 225 (1969), 195.
  13. D. Jasnow and M. E. Fisher, Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press), Vol. 4 (in press).
  14. M. Suzuki, Prog. Theor. Phys. 46 (1971), 1054[PTP].
  15. R. Abe, Prog. Theor. Phys. 44 (1970), 339[PTP].
  16. M. Suzuki, Prog. Theor. Phys. 56 (1976), 1007[PTP].
  17. B. I. Halperin, P. C. Hohenberg and S. Ma, Phys. Rev. B 10 (1974), 139[APS].
  18. M. Suzuki and G. Igarashi, Prog. Theor. Phys. 49 (1973), 1070[PTP].
    M. Suzuki, Prog. Theor. Phys. 50 (1973), 1767[PTP].
    M. Suzuki and F. Tanaka, Prog. Theor. Phys. 52 (1974), 722, [PTP]and references cited therein.
  19. M. Suzuki, Int. J. Magnetism 1 (1971), 123.
  20. K. Binder, Phys. Rev. B 8 (1973), 3423[APS].
  21. References cited in the first paper of Ref. 10).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 4218-4220 :
    Accurate Estimation of the Dynamical Critical Exponent of the Two-Dimensional Kinetic Ising Model Based on the Ising Machine m-TIS
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  2. Journal of the Physical Society of Japan 57 (1988) pp. 807-817 :
    Coherent-Anomaly Method in Critical Phenomena. V. Estimation of the Dynamical Critical Exponent Δ of the Two-Dimensional Kinetic Ising Model
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  3. Journal of the Physical Society of Japan 62 (1993) pp. 3052-3061 :
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    Macoto Kikuchi and Nobuyasu Ito
  4. Journal of the Physical Society of Japan 65 (1996) pp. 736-740 :
    Non-Equilibrium Critical Dynamics of the Kinetic Baxter Model
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  5. Journal of the Physical Society of Japan 66 (1997) pp. 3411-3420 :
    Nature of the Ordered Phase and the Critical Properties of the Three Dimensional Six-State Clock Model
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  6. Journal of the Physical Society of Japan 68 (1999) pp. 803-810 :
    Non-Universal Critical Behavior in the Ferromagnetic Transition of the ± J Ising Model
    Nobuyasu Ito, Yukiyasu Ozeki and Hidetsugu Kitatani
  7. Journal of the Physical Society of Japan 69 (2000) pp. 1931-1934 :
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  8. Journal of the Physical Society of Japan 70 (2001) pp. 3471-3474 :
    Numerical Evidence of Infinite Number of Pure States Near Ferromagnetic Phase Boundary for Short-Range Spin-Glass Systems
    Yukiyasu Ozeki, Nobuyasu Ito and Keita Ogawa
  9. Journal of the Physical Society of Japan 77 (2008) 014002 (5 pages) :
    Dynamic Critical Exponents of Three-Dimensional Ising Models and Two-Dimensional Three-States Potts Models
    Yohsuke Murase and Nobuyasu Ito
  10. Journal of the Physical Society of Japan 81 (2012) 074602 (8 pages) :
    Nonequilibrium Relaxation Study of Effect of Randomness on Critical Universality Classes of Ferromagnetic Phase Transitions
    Yukiyasu Ozeki, Satoshi Yotsuyanagi, and Nobuyasu Ito
  11. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 755-766 :
    Classical Representation and Scaling Property of the Kondo, Hubbard and Anderson Hamiltonians, and Quantal Random Systems
    Masuo Suzuki
  12. Progress of Theoretical Physics Vol. 60 No. 6 (1978) pp. 1669-1685 :
    Monte Carlo Simulation and Static and Dynamic Critical Behavior of the Plane Rotator Model
    Seiji Miyashita, Hidetoshi Nishimori, Akira Kuroda and Masuo Suzuki
  13. Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1573-1583 :
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    M. C. Yalabik and J. D. Gunton
  14. Progress of Theoretical Physics Vol. 68 No. 2 (1982) pp. 493-507 :
    Finite-Size Scaling Approach to the Kinetic Ising Model
    Hiroshi Takano
  15. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 65-76 :
    Phase Transition and Fractals
    Masuo Suzuki
  16. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1397-1400 :
    Finite-Size Scaling for Transient Similarity and Fractals
    Masuo Suzuki
  17. Progress of Theoretical Physics Vol. 73 No. 5 (1985) pp. 1122-1140 :
    Dynamical Nature of the Phase Transition of the Two-Dimensional Kinetic Ising Model
    Seiji Miyashita and Hiroshi Takano
  18. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1369-1376 :
    Order Parameter and Finite-Size Scaling
    Hiroshi Takano and Yukio Saito
  19. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 916-917 :
    Scaling Theory of Potts Model and Fractal Dimensions
    Mamoru Yamashita
  20. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1391-1401 :
    Fractal Configurations of the Two- and Three-Dimensional Ising Models at the Critical Point
    Nobuyasu Ito and Masuo Suzuki
  21. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 34-39 :
    The Critical Point within the Metastable Region in D=4 Z(2) Lattice Gauge Theory
    Yumi S. Hirata
  22. Progress of Theoretical Physics Supplement No.79 (1984) pp. 125-140 :
    Fluctuation and Formation of Macroscopic Order in Non-Equilibrium Systems
    Masuo Suzuki
  23. Progress of Theoretical Physics Supplement No.87 (1986) pp. 1-22 :
    Skeletonization, Fluctuating Mean-Field Approximations and Coherent Anomalies in Critical Phenomena
    Masuo Suzuki
  24. Progress of Theoretical Physics Supplement No.87 (1986) pp. 23-32 :
    Transfer Matrix and Finite-Size Scaling for the Ising Model on Two- and Three-Dimensional Lattices
    Takehiko Oguchi and Yoshihiro Taguchi
  25. Progress of Theoretical Physics Supplement No.138 (2000) pp. 555-560 :
    Non-Equilibrium Relaxation of Fluctuation
    Nobuyasu Ito, Keita Ogawa, Koji Hukushima and Yukiyasu Ozeki

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