Zeitschrift für Physik B Condensed Matter

, Volume 89, Issue 1, pp 79–87 | Cite as

Minimal renormalization without ε-expansion

Amplitude functions in three dimensions belowTc
  • F. J. Halfkann
  • V. Dohm
Original Contributions


The minimal subtraction scheme and the Borel resummation method are used to calculate the amplitudes of renormalized correlation functions belowT c for the three-dimensionalφ4 model with a oneccomponent order parameter. Accurate representations are given for the effective amplitudes of the renormalized expressions of the order parameter, of the susceptibility and of the specific heat. The resummed higher-order contributions to the order parameter,and to the specific heat turn out to yield only small corrections to the low-order approximations. Our results provide the basis for accurate analyses of the critical behavior of Ising-type systems in three dimensions belowT c including the amplitude functions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dohm, V.: Z. Phys. B-Condensed Matter60, 61 (1985)Google Scholar
  2. 2.
    Schloms, R., Dohm, V.: Europhys. Lett.3, 413 (1987)Google Scholar
  3. 3.
    Schloms, R., Dohm, V.: Nucl. Phys. B328, 639 (1989)Google Scholar
  4. 4.
    Krause, H.J., Schloms, R., Dohm, V.: Z. Phys. B—Condensed Matter79, 287 (1990);80, 313 (1990)Google Scholar
  5. 5.
    Schloms, R., Dohm, V.: Phys. Rev. B42, 6142 (1990)Google Scholar
  6. 6.
    Amit, D.J.: Field theory, the renormalization group and critical phenomena. Singapore: World Scientific 1984Google Scholar
  7. 7.
    Bagnuls, C., Bervillier, C., Meiron, D.I., Nickel, B.G.: Phys. Rev. B35, 3585 (1987)Google Scholar
  8. 8.
    De Dominics, C., Peliti, L.: Phys. Rev. B18, 353 (1978)Google Scholar
  9. 9.
    Dohm, V.: J. Low Temp. Phys.69, 51 (1987)Google Scholar
  10. 10.
    (In (2.21) we have corrected the previous [5],. definition ofP-(u), cf. (3.18) and (3.19) of [5], Schloms, R., Dohm, V.: Phys. Rev. B42, 6142 (1990) by the factor−1/2. See also Schloms, R., Dohm, V.: Phys. Rev. B, Erratum (1992)Google Scholar
  11. 11.
    Halfkann, F.J.: Diplomarbeit, TH Aachen 1991Google Scholar
  12. 12.
    Symanzik, K.: Lett. Nuovo Cimento8, 771 (1973)Google Scholar
  13. 13.
    Bergère, M.C., David, F.: Ann. Phys. (N.Y.)142, 416 (1982)Google Scholar
  14. 14.
    Bagnuls, C., Bervillier, C.: Phys. Rev. B32, 7209 (1985)Google Scholar
  15. 15.
    Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. B21, 3976 (1980); Zinn-Justin, J.: Phys. Rep.70, 109 (1981)Google Scholar
  16. 16.
    Greywall, D.S., Ahlers, G.: Phys. Rev. Lett.28, 1251 (1972); Phys. Rev. A7, 2145 (1973)Google Scholar
  17. 17.
    Ahlers, G.: Phys. Rev. A3, 696 (1971)Google Scholar
  18. 18.
    Mueller, K.H., Ahlers, G., Pobell, F.: Phys. Rev. B14, 2096 (1976)Google Scholar
  19. 19.
    Lipa, J.A., Chui, T.C.P.: Phys. Rev. Lett.51, 2291 (1983)Google Scholar
  20. 20.
    Tam, W.Y., Ahlers, G.: Phys. Rev. B32, 5932 (1985);33, 183 (1986);37, 7898 (1988)Google Scholar
  21. 21.
    Dohm, V.: Phys. Rev. Lett.53, 1379, 2520 (1984); In: Proceedings of the Seventeenth International Conference on Low Temperature Physics. Eckern, U., Schmidt, A., Weber, W., Wühl, H. (eds.), p. 953. Amsterdam: North Holland 1984Google Scholar
  22. 22.
    Schloms, R., Eggers, J., Dohm, V.: Jpn. J. Appl. Phys. [Suppl.]26–3, 49 (1987)Google Scholar
  23. 23.
    Dohm, V.: Phys. Rev. B44, 2697 (1991)Google Scholar
  24. 24.
    Bervillier, C.: Private communicationGoogle Scholar
  25. 25.
    Lipatov, L.N.: Zh. Eksp. Teor. Fiz.72, 411 (1977) [Sov. Phys.-JEPT45, 216 (1977)]; Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. D15, 1544 (1977)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • F. J. Halfkann
    • 1
  • V. Dohm
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Hochschule AachenAachenFederal Republic of Germany

Personalised recommendations