Zeitschrift für Physik B Condensed Matter

, Volume 79, Issue 2, pp 287–293 | Cite as

Minimal renormalization without ɛ-expansion: Amplitude functions in three dimensions

  • H. J. Krause
  • R. Schloms
  • V. Dohm
Original Contributions

Abstract

The minimal subtraction scheme and the Borel resummation method are used to calculate the amplitudes of renormalized correlation functions aboveT c for then-vector model in three dimensions. Accurate representations are given for the effective amplitudes of the renormalized expressions of the correlation length, of the susceptibility and of the specific heat forn=1, 2, 3. The resummed higher-order contributions turn out to yield only small corrections to the low-order approximations. These results complement a recent calculation of renormalization-group functions and provide the basis for accurate analyses of the critical behavior in three dimensions including the amplitude functions.

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References

  1. 1.
    't Hooft, G.: Nucl. Phys. B61, 455 (1973); 't Hooft, G., Veltman, M.: Nucl. Phys. B44, 189 (1972)Google Scholar
  2. 2.
    Amit, D.J.: Field theory, the renormalization group and critical phenomena. New York: McGraw-Hill 1978; Singapore: World Scientific 1984Google Scholar
  3. 3.
    Schloms, R., Dohm, V.: Nucl. Phys. B328, 639 (1989)Google Scholar
  4. 4.
    Schloms, R., Dohm, V.: (to be published)Google Scholar
  5. 5.
    Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. B21, 3976 (1980); Zinn-Justin, J.: Phys. Rep.70, 109 (1981)Google Scholar
  6. 6.
    Dohm, V.: Z. Phys. B-Condensed Matter60, 61 (1985)Google Scholar
  7. 7.
    Schloms, R., Dohm, V.: Europhys. Lett.3, 413 (1987)Google Scholar
  8. 8.
    Dohm, V.: Phys. Rev. Lett.53, 1379, 2520 (1984); In: Proceedings of the Seventeenth International Conference on Low Temperature Physics. Eckern, U., Schmid, A., Weber, W., Wühr, H. (eds.), p. 953. Amsterdam: North Holland 1984Google Scholar
  9. 9.
    Schloms, R., Eggers, J., Dohm, V.: Jpn. J. Appl. Phys. Suppl.26-3, 49 (1987)Google Scholar
  10. 10.
    Bagnuls, C., Bervillier, C.: Phys. Rev. B32, 7209 (1985)Google Scholar
  11. 11.
    De Dominicis, C., Peliti, L.: Phys. Rev. B18, 353 (1978)Google Scholar
  12. 12.
    Dohm, V.: J. Low Temp. Phys.69, 51 (1987)Google Scholar
  13. 13.
    Wilson, K.G., Kogut, J.B.: Phys. Rep.12C, 75 (1974)Google Scholar
  14. 14.
    Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: In: Phase transitions and critical phenomena. Domb, C., Green, M.S. (eds.), Vol. VI. New York: Academic Press 1976Google Scholar
  15. 15.
    Dohm, V.: In: Applications of field theory to statistical mechanics. Garrido, L. (ed.), p. 263. Berlin, Heidelberg, New York: Springer 1985. The r.h.s. of Eq. (6) of this paper should be multiplied byK d−1 Google Scholar
  16. 16.
    Ahlers, G.: Phys. Rev. A3, 696 (1971)Google Scholar
  17. 17.
    Mueller, K.H., Ahlers, G., Pobell, F.: Phys. Rev. B14, 2096 (1976)Google Scholar
  18. 18.
    Lipa, J.A., Chui, T.C.P.: Phys. Rev. Lett.51, 2291 (1983)Google Scholar
  19. 19.
    Greywall, D.S., Ahlers, G.: Phys. Rev. Lett.28, 1251 (1972); Phys. Rev. A7, 2145 (1973)Google Scholar
  20. 20.
    Singsaas, A., Ahlers, G.: Phys. Rev. B30, 5103 (1984)Google Scholar
  21. 21.
    Dohm, V.: Z. Phys. B-Condensed Matter61, 193 (1985); Tam, W.Y., Ahlers, G.: Phys. Rev. B33, 183 (1986); B37, 7898 (1988)Google Scholar
  22. 22.
    Nickel, B.G., Meiron, D.I., Baker, G.A.: University of Guelph report (1977), unpublishedGoogle Scholar
  23. 23.
    Bervillier, C., Godrèche, C.: Phys. Rev. B21, 5427 (1980)Google Scholar
  24. 24.
    Vladimirov, A.A., Kazakov, D.I., Tarasov, O.V.: Sov. Phys. JETP50, 521 (1979)Google Scholar
  25. 25.
    Chetyrkin, K.G., Gorishny, S.G., Larin, S.A., Tkachov, F.V.: Phys. Lett.132B, 351 (1983); Gorishny, S.G., Larin, S.A., Tkachov, F.V.: Phys. Lett.101A, 120 (1984)Google Scholar
  26. 26.
    Chetyrkin, K.G., Kataev, A.L., Tkachov, F.V.: Phys. Lett.99B, 147 (1981);101B, 457 (1981); Kazakov, D.I.: Phys. Lett.133B, 406 (1983)Google Scholar
  27. 27.
    Nicoll, J.F., Albright, P.C.: Phys. Rev. B31, 4576 (1985)Google Scholar
  28. 28.
    Lipatov, L.N.: Zh. Eksp. Teor. Fiz.72, 411 (1977) [Sov. Phys. JETP45, 216 (1977)]; Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. D15, 1544 (1977)Google Scholar
  29. 29.
    Krause, H.J.: Diplomarbeit, TH Aachen (1989)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • H. J. Krause
    • 1
  • R. Schloms
    • 1
  • V. Dohm
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Hochschule AachenFederal Republic of Germany

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