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Prog. Theor. Phys. Vol. 49 No. 2 (1973) pp. 442-452

[ Full Text PDF : FREE ACCESS (630K) ]

Critical Exponents and Scaling Relations in 1/n Expansion

Ryuzo Abe and Shinobu Hikami

Departmet of Pure and Applied Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo

(Received September 9, 1972)

Abstract:

The critical exponents ν, η and α are derived in powers of 1/n to first order for the n-vector model (or n-component system) with short-range interactions. Scaling relations χ(q)∼ε-γf(q/εν), dν=d-α and γ=ν(2-η) are confirmed up to the order of 1/n.


URL : http://ptp.ipap.jp/link?PTP/49/442/
DOI : 10.1143/PTP.49.442

[ Full Text PDF : FREE ACCESS (630K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 49 No. 3 (1973) pp. 1074-1075 :
    Critical Exponent η up to 1/n2 for the Three-Dimensional System with Short-Range Interaction
    Ryuzo Abe
  2. Progress of Theoretical Physics Vol. 49 No. 4 (1973) pp. 1096-1105 :
    Critical Exponents and Scaling Relations in 1/n Expansion. II
    Shinobu Hikami
  3. Progress of Theoretical Physics Vol. 49 No. 4 (1973) pp. 1106-1120 :
    Critical Exponents for Long-Range Interactions. II
    Masuo Suzuki
  4. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1440-1450 :
    Critical Exponents for Long-Range Interactions. III
    Masuo Suzuki
  5. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1451-1458 :
    Critical Behavior of the Anisotropic Classical n-Vector Model
    Masuo Suzuki
  6. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 1851-1857 :
    Breakdown of Some Scaling Law Relations in 1/n Expansion
    Ryuzo Abe and Shinobu Hikami
  7. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 1877-1888 :
    Critical Exponent η up to 1/n2 for the Three-Dimensional System with Short-Range Interaction
    Ryuzo Abe
  8. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 393-408 :
    On the Expansion Theory of Critical Exponents
    Masuo Suzuki
  9. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1041-1052 :
    Discontinuities of Critical Amplitude for Specific Heat
    Ryuzo Abe and Shinobu Hikami
  10. Progress of Theoretical Physics Vol. 52 No. 1 (1974) pp. 344-346 :
    Critical Dynamics in Bose Systems
    Masuo Suzuki and Fumihiko Tanaka
  11. 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
  12. Progress of Theoretical Physics Vol. 52 No. 4 (1974) pp. 1135-1145 :
    Quantum Effect, Critical Dynamics and One-Particle Excitation in 1/n Expansion. I
    Ryuzo Abe
  13. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1431-1437 :
    Critical Behavior of an Extremely Anisotropic n-Vector Model
    Shinobu Hikami
  14. 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
  15. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 325-332 :
    Scaling Function for Critical Scattering in 1/n Expansion
    Ryuzo Abe and Shinobu Hikami
  16. 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
  17. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1108-1115 :
    Critical Behavior of Classical n-Vector Model near Zero Temperature
    Shinobu Hikami
  18. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 785-796 :
    Fixed Points and Anomalous Dimensions in a Thirring-Type Model in 2+ε Dimensions
    Shinobu Hikami and Taizo Muta
  19. Progress of Theoretical Physics Vol. 57 No. 4 (1977) pp. 1197-1208 :
    Equation of State in 1/n Expansion
    Ryuzo Abe and Shinobu Hikami
  20. 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
  21. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1705-1719 :
    Anomalous Dimensions of Composite Operators in the Gross-Neveu Model in 2+ε Dimensions
    Taizo Muta and Dragan S. Popović
  22. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 506-515 :
    Fixed Points of a Coupled Order System in 1/n Expansion
    Shinobu Hikami
  23. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 386-392 :
    Logarithmic Corrections to a Simple Power Law at d = 4 in 1/n Expansion
    Yutaka Okabe
  24. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 742-750 :
    1/n Expansion for Weakly Random System
    Ryuzo Abe
  25. 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
  26. 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
  27. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 98-106 :
    Some Remarks on the n=0 Problem in Critical Phenomena
    Ryuzo Abe
  28. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 226-233 :
    Renormalization Group Functions of CPN-1 Non-Linear σ-Model and N-Component Scalar QED Model
    Shinobu Hikami
  29. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 813-819 :
    Modification of 1/n Expansion in Critical Phenomena
    Ryuzo Abe
  30. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1425-1434 :
    Non-Linear σ Model of Grassmann Manifold and Non-Abelian Gauge Field with Scalar Coupling
    Shinobu Hikami
  31. 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
  32. Progress of Theoretical Physics Vol. 72 No. 4 (1984) pp. 736-745 :
    The 1/n Expansion for the Extraordinary Transition of Semi-Infinite System
    Kaoru Ohno and Yutaka Okabe
  33. Progress of Theoretical Physics Vol. 121 No. 5 (2009) pp. 897-914 :
    1/n Expansion of the Random Easy Axis Model. II
    Kazuo Ideura

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