Ring Diagram Contribution to Electron Correlations

  • A. Isihara


The ring diagram contribution to the correlation energy of an electron gas in 3-D and in 2-D is treated in an accurate and systematic way by applying the Montroll and Ward formula for the grand partition function. Difficulties in the traditional rg series are pointed out and a new direct method of evaluation is discussed. The ring diagram formula can be derived in different ways without using diagrams.


Coulomb Interaction Ground State Energy Electron Correlation Correlation Energy Order Exchange 
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  1. 1.
    F. Bloch, Z. Physik,57, 545 (1929).Google Scholar
  2. 2.
    E. P. Wigner, Phys. Rev., 46, 1002 (1934); Trans. Farad. Soc. 34, 678 (1938); K. Fuchs, Proc. Roy. Soc.(London), 151, 585 (1935).Google Scholar
  3. 3.
    W. Macke, Z. Naturforsch.,5a, 192 (1950); D. Pines, Phys. Rev., 92, 626 (1953).Google Scholar
  4. 4.
    M. Gell-Mann and K. Brueckner, Phys. Rev.,106, 364 (1957); P. Nozieres and D. Pines, ibid, 111, 442 (1958); J. Hubbard, Proc. Roy. Soc.(London), A243, 336 (1958); A. Isihara and E. W. Montroll, Proc. Nat. Acad. Sci., 68, 3111 (1971).Google Scholar
  5. 5.
    E. W. Montroll and J. C. Ward, Phys. Fluids, 1 55 (1958)Google Scholar
  6. 6.
    D. F. Du Bois, Ann. Phys.,N.Y. 8, 24 (1959).Google Scholar
  7. 7.
    W. Carr and A. A. Maradudin, Phys. Rev.,133A, 371 (1964).Google Scholar
  8. 8.
    A. Isihara, “Statistical Physics”, ( Academic Press, N.Y., 1971 ), p. 302.Google Scholar
  9. 9.
    A. Isihara and D. Y. Kojima, Phys. Cond. Matter,18, 249 (1974); Zeits. f. Phys.,B21, 33 (1975).Google Scholar
  10. 10.
    A. Isihara and D. Y. Kojima, Phys. Rev.,B11, 710 (1975).Google Scholar
  11. 11.
    A. L. Fetter and J. D. Walecka,“Quantum Theory of Many-Particle Systems”, (McGraw-Hill, N.Y., 1971), p. 166, p. 287.Google Scholar
  12. 12.
    A. Isihara, “Statistical Physics”, ( Academic Press, N.Y., 1971 ), p. 415.Google Scholar
  13. 13.
    A. Isihara and T. Toyoda, Zeits, f. Phys.,B23, 389 (1976).Google Scholar
  14. 14.
    D.Y. Kojima and A.Isihara, Phys.Cond. Matter, 18, 121 (1974).Google Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • A. Isihara
    • 1
  1. 1.Statistical Physics Laboratory, Department of PhysicsState University of New York at BuffaloBuffaloUSA

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