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Prog. Theor. Phys. Vol. 49 No. 4 (1973) pp. 1096-1105

[ Full Text PDF : FREE ACCESS (511K) ]

Critical Exponents and Scaling Relations in 1/n Expansion. II

— Classical n-Vector Model with Short-Range Interaction —

Shinobu Hikami

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

(Received September 30, 1972)

Abstract:

The critical exponents δ and Δ are derived in powers of 1/n to first order for the n-vector model with short range interactions. Scaling relations α=2+γ-Δ, δ=(d+2-η)/(d-2+η) and δ=Δ/(Δ-2γ) are confirmed exactly up to order 1/n. By considering successive derivatives of magnetization with respect to external field and temperature, the equations of state above the critical point M=∑∞m=0cmε-γ-(m-1)ΔH2m-1 and M=∑∞m=0amH1-2(γ+m)/δεm are confirmed up to order 1/n.


URL : http://ptp.ipap.jp/link?PTP/49/1096/
DOI : 10.1143/PTP.49.1096

[ Full Text PDF : FREE ACCESS (511K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 49 (1973), 113[PTP].
  2. R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
  3. C. Domb and D. H. Hunter, Proc. Phys. Soc. 86 (1965), 1147.
  4. M. Ferer, M. A. Moore and M. Wortis, Phys. Rev. B 4 (1971), 3954[APS].
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  6. R. Abe, Prog. Theor. Phys. 38 (1967), 72[PTP].
  7. P. Schofield, Phys. Rev. Lett. 22 (1969), 606[APS].
  8. D. S. Gaunt and C. Domb, J. Phys. C 3 (1970), 1442[IoP STACKS].
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1440-1450 :
    Critical Exponents for Long-Range Interactions. III
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1451-1458 :
    Critical Behavior of the Anisotropic Classical n-Vector Model
    Masuo Suzuki
  3. 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
  4. 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
  5. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 393-408 :
    On the Expansion Theory of Critical Exponents
    Masuo Suzuki
  6. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1041-1052 :
    Discontinuities of Critical Amplitude for Specific Heat
    Ryuzo Abe and Shinobu Hikami
  7. 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
  8. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1431-1437 :
    Critical Behavior of an Extremely Anisotropic n-Vector Model
    Shinobu Hikami
  9. Progress of Theoretical Physics Vol. 57 No. 4 (1977) pp. 1197-1208 :
    Equation of State in 1/n Expansion
    Ryuzo Abe and Shinobu Hikami
  10. 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
  11. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 742-750 :
    1/n Expansion for Weakly Random System
    Ryuzo Abe

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