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Prog. Theor. Phys. Vol. 49 No. 6 (1973) pp. 1877-1888

[ Full Text PDF : FREE ACCESS (739K) ]

Critical Exponent η up to 1/n2 for the Three-Dimensional System with Short-Range Interaction

Ryuzo Abe

Department of Pure and Applied Sciences, University of Tokyo, Komaba, Meguro-Ku, Tokyo

(Received January 22, 1973)

Abstract:

By means of the 1/n expansion method, the critical exponent η is discussed for the three-dimensional isotropic n-vector model with short-range interaction. Terms up to 1/n2 are obtained and the result is compared with the numerical estimate based on high temperature expansion and with Wilson's ε expansion.


URL : http://ptp.ipap.jp/link?PTP/49/1877/
DOI : 10.1143/PTP.49.1877

[ Full Text PDF : FREE ACCESS (739K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 48 (1972), 1414[PTP]; ibid. 49 (1973), 113[PTP]. The latter paper is referred to as A.
  2. R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
  3. S. Hikami, Prog. Theor. Phys. 49 (1973), 1096[PTP].
  4. S. Ma, Phys. Rev. Lett. 29 (1972), 1311[APS]; University of California preprint.
  5. M. E. Fisher, S. Ma and B. G. Nickel, Phys. Rev. Lett. 29 (1972), 917[APS].
  6. M. Suzuki, Phys. Lett. A 42 (1972), 5[CrossRef]; Prog. Theor. Phys. 49 (1973), 424[PTP]; ibid. 49 (1973), 1106[PTP].
  7. E. Brézin and D. J. Wallace, Princeton University preprint.
  8. R. Abe and S. Hikami, Phys. Lett. A 42 (1973), 419[CrossRef].
  9. R. A. Ferrell and D. J. Scalapino, Phys. Rev. Lett. 29 (1972), 413[APS]; Phys. Lett. A 41 (1972), 371[CrossRef].
  10. K. G. Wilson, Phys. Rev. Lett. 28 (1972), 548[APS].
  11. L. P. Kadanoff and F. J. Wegner, Phys. Rev. B 4 (1971), 3989[APS].
    M. Suzuki, Phys. Rev. Lett. 28 (1972), 507[APS].
  12. Cited from Ref. 10).
  13. See, for example, P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, 1953), p. 1083.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 393-408 :
    On the Expansion Theory of Critical Exponents
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1041-1052 :
    Discontinuities of Critical Amplitude for Specific Heat
    Ryuzo Abe and Shinobu Hikami
  3. Progress of Theoretical Physics Vol. 52 No. 2 (1974) pp. 369-378 :
    Crossover Exponent of the Spin Anisotropic n-Vector Model with Short-Range Interaction in 1/n Expansion
    Shinobu Hikami and Ryuzo Abe
  4. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1431-1437 :
    Critical Behavior of an Extremely Anisotropic n-Vector Model
    Shinobu Hikami
  5. Progress of Theoretical Physics Vol. 54 No. 5 (1975) pp. 1570-1572 :
    Critical Exponents in Three Dimensions
    Toshihiko Tsuneto and Shin Ueno
  6. Progress of Theoretical Physics Vol. 54 No. 6 (1975) pp. 1693-1706 :
    Study of Specific Heat below Tc in 1/n Expansion
    Ryuzo Abe and Shinobu Hikami
  7. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1538-1546 :
    Consistency for a Critical Amplitude Ratio Rχ in 1/n and ε Expansions
    Ryuzo Abe and Shinobu Hikami
  8. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 1825-1833 :
    1/n Expansion up to Order 1/n2. I
    Yutaka Okabe, Michiyoshi Oku and Ryuzo Abe
  9. Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1277-1286 :
    1/n Expansion Up to Order 1/n2. II
    Yutaka Okabe and Michiyoshi Oku
  10. Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1287-1297 :
    1/n Expansion Up to Order 1/n2. III
    Yutaka Okabe and Michiyoshi Oku
  11. Progress of Theoretical Physics Vol. 63 No. 5 (1980) pp. 1528-1540 :
    Spherical Limit of Coupled Time-Dependent n-Vector Models. I
    Michiyoshi Oku
  12. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 813-819 :
    Modification of 1/n Expansion in Critical Phenomena
    Ryuzo Abe
  13. 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
  14. Progress of Theoretical Physics Vol. 65 No. 4 (1981) pp. 1191-1197 :
    Effect of Weak Randomness on Corrections to Scaling
    Yutaka Okabe
  15. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 1947-1958 :
    Two-Dimensional Defect in Three-Dimensional Lattice
    Kazuhisa Yamamoto and Ryuzo Abe
  16. Progress of Theoretical Physics Vol. 69 No. 2 (1983) pp. 464-479 :
    Higher Order Calculations for d-Dimensional Lattice with d′-Dimensional Defect
    Ryuzo Abe, Kazuhisa Yamamoto and Kazuo Ideura
  17. Progress of Theoretical Physics Vol. 85 No. 3 (1991) pp. 509-525 :
    Zeros of Partition Function and High Temperature Expansion for the Two-Dimensional Ising Models
    Ryuzo Abe, Tomonari Dotera and Takeshi Ogawa
  18. Progress of Theoretical Physics Vol. 95 No. 2 (1996) pp. 409-420 :
    The Effectiveness of the Local Potential Approximation in the Wegner-Houghton Renormalization Group
    Ken-Ichi Aoki, Keiichi Morikawa, Wataru Souma, Jun-Ichi Sumi and Haruhiko Terao

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