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Prog. Theor. Phys. Vol. 59 No. 3 (1978) pp. 742-750

[ Full Text PDF : FREE ACCESS (502K) ]

1/n Expansion for Weakly Random System

Ryuzo Abe

Department of Pure and Applied Sciences, College of General Education, University of Tokyo, Komaba, Meguro-ku, Tokyo 153

(Received November 4, 1977)

Abstract:

This paper is concerned with 1/n expansion for a random spin system. The interaction between the i-th and the j-th site is assumed to be \hatKij = Kij(1-api)(1-apj) where pi is a random variable. By assuming that a is small (weakly random case), the partition function in the presence of magnetic field is expanded in a double series of 1/n and a for the quenched case. The equation of state is derived up to a2 in the limit n →∞. It is shown that critical exponents take their spherical model values up to this order.


URL : http://ptp.ipap.jp/link?PTP/59/742/
DOI : 10.1143/PTP.59.742

[ Full Text PDF : FREE ACCESS (502K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 58 (1977), 1722[PTP].
  2. M. E. Fisher, Phys. Rev. Lett. 30 (1973), 679[APS].
  3. R. Abe and S. Hikami, Prog. Theor. Phys. 57 (1977), 1197[PTP].
  4. R. Abe, Prog. Theor. Phys. 49 (1973), 113[PTP].
  5. R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
  6. S. Hikami, Prog. Theor. Phys. 49 (1973), 1096[PTP].
  7. Y. Okabe and M. Masutani, Phys. Lett. A 65 (1978), 97[CrossRef].
  8. R. Abe and S. Hikami, Prog. Theor. Phys. 54 (1975), 1693[PTP].
  9. R. Abe and S. Hikami, Prog. Theor. Phys. 51 (1974), 1041[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1478-1482 :
    Scaling Function for Equation of State
    Ryuzo Abe
  2. Progress of Theoretical Physics Vol. 62 No. 5 (1979) pp. 1236-1244 :
    Critical Exponent Induced by Impurity Effect
    Ryuzo Abe
  3. Progress of Theoretical Physics Vol. 65 No. 4 (1981) pp. 1179-1190 :
    Higher-Order Calculations for Weakly Random System in 1/n Expansion
    Kazuo Ideura, Yutaka Okabe and Ryuzo Abe
  4. Progress of Theoretical Physics Vol. 65 No. 4 (1981) pp. 1237-1245 :
    d'-Dimensional Defect in d-Dimensional Lattice. I
    Ryozo Abe
  5. Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 1835-1843 :
    d'-Dimensional Defect in d-Dimensional Lattice. II
    Ryuzo Abe
  6. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 77-89 :
    Quenched System in the Spherical Limit of the Random n-Vector Model
    Michiyoshi Oku
  7. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1604-1611 :
    1/ n Expansion for Weakly Random System with Impurity Correlation
    Kazuhisa Yamamoto and Ryuzo Abe
  8. Progress of Theoretical Physics Vol. 67 No. 1 (1982) pp. 118-130 :
    Gaussian Random Bond Problem for Annealed System in 1/n Expansion
    Michiyoshi Oku and Ryuzo Abe
  9. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 707-713 :
    Equation for Pair Correlation Function of n-Vector Model
    Ryuzo Abe

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