Advertisement

Theoretical and Mathematical Physics

, Volume 52, Issue 1, pp 712–721 | Cite as

Correlation functions of a Heisenberg ferromagnet in the paramagnetic region

  • Yu. A. Tserkovnikov
Article

Conclusions

In the present paper, in the framework of the coupled-mode approximation for the second-order equations (2.6)–(2.9) we have obtained an approximate closed system of equations (2.10)–(2.14) for the spin correlation functions of a Heisenberg ferromagnet in a vanishing external magnetic field and at temperatures θ above the critical temperature (θ≥θ c )., In principle, Eqs. (2.10)–(2.14) make it possible to investigate the behavior of the correlation functions in the entire investigated temperature range, including the critical point. Equations (2.10)–(2.14) are very complicated, and a numerical calculation is needed to analyze them.

In the fourth section, we obtained interpolation formulas that make it possible to describe in some detail the behavior of the spectral density at both high and low frequencies. It would be expedient to find first the solution, of the simplified system of equations obtained from (2.10)–(2.14) by replacement of the Green's function (2.10) and the spectral density (3.2) by their interpolation expressions (4.2) and (4.3). Substituting (4.3) in (3.3) and (3.4), we obtain equations for λ and Δ, in terms of which all the remaining quantities can be expressed. The solution obtained from the simplified system can be used further as initial approximation in the solution of the system of equations (2.10)–(2.14). However, this problem goes beyond the framework of the given paper.

Keywords

Magnetic Field Correlation Function Numerical Calculation Critical Temperature Spectral Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    R. Brout, Phys. Lett. A,24, 117 (1967).Google Scholar
  2. 2.
    J. L. Beeby and J. Hubbard, Phys. Lett. A,26, 376 (1968).Google Scholar
  3. 3.
    K. Kawasaki, J. Phys. Chem. Solids,28, 1277 (1967).Google Scholar
  4. 4.
    B. I. Halperin and P. C. Hohenberg, Phys. Rev.,188, 898 (1969).Google Scholar
  5. 5.
    R. H. Knapp (Jr) and D. ter Haar, J. Stat. Phys.,1, 149 (1969) (see also: Problems of Theoretical Physics [in Russian], (dedicated to N. N. Bogolyubov on the occasion of his 60th birthday), Nauka, Moscow (1969), pp. 341–348).Google Scholar
  6. 6.
    S. A. Scales and H. A. Gersch, J. Stat. Phys.,7, 95 (1973).Google Scholar
  7. 7.
    K. Fujii, I. Mannari, and S. Kadowaki, Prog. Theory. Phys.,50, 1501 (1973).Google Scholar
  8. 8.
    Yu. G. Rudoi, Teor. Mat. Fiz.,26, 387 (1976).Google Scholar
  9. 9.
    Yu. A. Tserkovnikov, Teor. Mat. Fiz.,40, 251 (1979).Google Scholar
  10. 10.
    Yu. A. Tserkovnikov, Dokl. Akad. Nauk SSSR,143, 832 (1962).Google Scholar
  11. 11.
    Yu. A. Tserkovnikov, Teor. Mat. Fiz.,49, 219 (1981).Google Scholar
  12. 12.
    Yu. A. Tserkovnikov, Teor. Mat. Fiz.,50, 261 (1982).Google Scholar
  13. 13.
    H. Mori, Prog. Theor. Phys.,34, 399 (1965).Google Scholar
  14. 14.
    V. P. Kalashnikov, Teor. Mat. Fiz.,34, 412 (1978).Google Scholar
  15. 15.
    R. Kubo, J. Phys. Soc. Jpn,12, 570 (1957).Google Scholar
  16. 16.
    D. N. Zubarev, Usp. Fiz. Nauk,71, 71 (1960).Google Scholar
  17. 17.
    N. N. Bogolyubov, Preprint R-1451 [in Russian], JINR, Dubna (1963).Google Scholar
  18. 18.
    A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Englewood Cliffs (1963).Google Scholar
  19. 19.
    S. H. Liu, Phys. Rev. B,13, 2979 (1976).Google Scholar
  20. 20.
    T. Schneider, Phys. Rev. B,7, 201 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Yu. A. Tserkovnikov

There are no affiliations available

Personalised recommendations