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Volumn 63, Issue 5, 2001, Pages

Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CORRELATION THEORY; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

EID: 0035335674     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056113     Document Type: Article
Times cited : (26)

References (79)
  • 13
    • 85035300236 scopus 로고    scopus 로고
    • Leningrad Nuclear Physics Institute Report 1976 (unpublished)
    • L. N. Lipatov, Leningrad Nuclear Physics Institute Report, 1976 (unpublished).
    • Lipatov, L.N.1
  • 17
    • 85035300872 scopus 로고    scopus 로고
    • H. Kleinert and V. Schulte-Frohlinde, Critical Properties of(Formula presented) Theories (World Scientific, Singapore, 2001), http://www.physik.fu-berlin.de/∼kleinert/b8
    • H. Kleinert and V. Schulte-Frohlinde, Critical Properties of(Formula presented) Theories (World Scientific, Singapore, 2001), http://www.physik.fu-berlin.de/∼kleinert/b8.
  • 28
    • 85035289373 scopus 로고    scopus 로고
    • e-print hep-th/0002136
    • See also J. Zinn-Justin, e-print hep-th/0002136.
    • Zinn-Justin, J.1
  • 41
    • 0000948326 scopus 로고
    • The presence and origin of confluent singular terms have been first understood from renormalization group analysis by F. J. Wegner, Phys. Rev. B 5, 4529 (1972).
    • (1972) Phys. Rev. B , vol.5 , pp. 4529
    • Wegner, F.J.1
  • 42
    • 0001410602 scopus 로고
    • (The ratio of the leading amplitude ratio for the heat capacity is incorrect in this later reference, as it is in 27
    • Phys. Rev. BFor a determination of the critical behavior of the first confluent singular term for the specific heat to the order (Formula presented), see M.-C. Chang and A. Houghton, 21, 1881 (1980) (The ratio of the leading amplitude ratio for the heat capacity is incorrect in this later reference, as it is in 27.
    • (1980) Phys. Rev. B , vol.21 , pp. 1881
    • Chang, M.-C.1    Houghton, A.2
  • 43
    • 0000815104 scopus 로고
    • or Appendix C of Ref. 25
    • Phys. Rev. BFor the corrected value for (Formula presented), see 31, which also gives other various confluent terms and gives references to other wrong ratios in the literature. For the corrected value of (Formula presented) for all N, see C. Bervillier, 34, 8141 (1986), or Appendix C of Ref. 25.)
    • (1986) Phys. Rev. B , vol.34 , pp. 8141
    • Bervillier, C.1
  • 46
    • 0011050681 scopus 로고
    • G. M. Avdeeva and A. A. Migdal, Pis’ma Zh. Éksp. Teor. Fiz. 16, 253 (1972) [JETP Lett. 16, 178 (1972)];
    • (1972) JETP Lett. , vol.16 , pp. 178
    • Avdeeva, G.M.1    Migdal, A.A.2
  • 58
    • 85035290291 scopus 로고    scopus 로고
    • See Chang and Houghton in Ref. 29
    • See Chang and Houghton in Ref. 29.
  • 64
    • 85035254216 scopus 로고    scopus 로고
    • H. KLeinert and B. Van den Bossche (unpublished)
    • H. KLeinert and B. Van den Bossche (unpublished).
  • 70
    • 85035292095 scopus 로고    scopus 로고
    • Note that the calculation we do in this paper are based on the normalization of the coupling constant of Dohm and co-workers 42 41 46 which differ from Kleinert’s 5 13. The difference in conventions disappears at the level of the exponents, and the value of (Formula presented) is only different by a factor 12, as mentioned after Eq. (11)
    • Note that the calculation we do in this paper are based on the normalization of the coupling constant of Dohm and co-workers 424146 which differ from Kleinert’s 513. The difference in conventions disappears at the level of the exponents, and the value of (Formula presented) is only different by a factor 12, as mentioned after Eq. (11).


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