Skip to main content
Log in

Lattice Green's Function for the Face Centered Cubic Lattice

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

An expression for the Green's function (GF) of face centered cubic (FCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bateman Manuscript Project (1963). Higher Transcendental Functions, Vol. I. A. Erdelyi et al., ed., McGraw-Hill, New York.

  • Berlin, T. H. and Kac, M. (1952). The spherical model of a ferromagent, Physical Review 86, 821.

    Google Scholar 

  • Brout, R. (1960). Statistical mechanical theory of ferromagnetism. High density behavior. Physical Review. 118, 1009.

    Google Scholar 

  • Domb, C. and Joyce, G. S. (1972). Cluster expansion for a polymer chain. Journal of Physics C: Solid State Physics 5, 956.

    Google Scholar 

  • Doniach, S. and Sondheimer, E. H. (1974). Green's Functions for Solid State Physicists, Benjamin, Reading, Massachusetts.

    Google Scholar 

  • Economou, E. N. (1983). Green Function in Quantum Physics, 2nd Edition, Springer-Verlag, Berlin.

    Google Scholar 

  • Gradshteyn, I. S. and Ryzhik, I. M. (1965). Tables of Integrals, Series, and Products, Academic, New York.

    Google Scholar 

  • Hijjawi, R. S. and Khalifeh, J. M. (2002). Remarks on the lattice Green's function, the general Glasser case. Journal of Theoretical Physics 41, 1769.

    MathSciNet  Google Scholar 

  • Inoue, M. (1974). Lattice Green's function for the face centered cubic lattice. Journal of Mathematical Physics 15, 704.

    Article  Google Scholar 

  • Joyce, G. S. (1971). Lattice Green's function for the anisotropic face centered cubic lattice. Journal of Physics C: Solid State Physics 4, L53.

    Article  ADS  Google Scholar 

  • Katsura, S., Morita, T., Inawashiro, S., Horiguci, T., and Abe, Y. (1971). Lattice Green's function (Introduction). Journal of Mathematical Physics 12, 892.

    Google Scholar 

  • Li, Q., Soukoulis, C., Economou, E. N., and Grest, G. S. (1989). An isotropic tight-binding model for localization. Physical Review B 40, 2825.

    ADS  Google Scholar 

  • Mano, K. (1974). Remarks on the Green's function for face-centered cubic lattices. Journal of Mathematical Physics 15, 2175.

    Article  MathSciNet  Google Scholar 

  • Mano, K. (1975). Remarks on the Green's function for cubic lattices. Journal of Mathematical Physics 16, 1726.

    Article  MathSciNet  ADS  Google Scholar 

  • Mattis, D. C. (1965). The Theory of Magnetism, Harper and Row, New York.

    Google Scholar 

  • Montroll, E. W. (1956). Proceedings of 3rd Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, ed., vol. 3, University of California Press, Berkeley, California, pp. 209–246.

  • Montroll, E. W. and Wiess, G. W. (1965). Journal of Mathematical Physics 6, 167.

    Article  Google Scholar 

  • Morita, T. and Horiguci, T. (1971a). Calculation on the lattice Green's function for the BCC, FCC, and rectangular lattices. Journal of Mathematical Physics 12, 986.

    Google Scholar 

  • Morita, T., and Horiguci, T. (1971b). Lattice Green's function for cubic lattices in terms of complete elliptic integral. Journal of Mathematical Physics 12, 981.

    Google Scholar 

  • Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (submitted). Applications on the Lattice Green's Functions for One and Two Dimensional Lattices.

  • Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002a). Remarks on the lattice Green's function, the Glasser case. Journal of Mathematical Physics 43, 1.

    Article  MathSciNet  Google Scholar 

  • Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002b). Remarks on the lattice Green's function for the body centered cubic lattice. Journal of Theoretical Physics 41, 973.

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. S. Hijjawi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hijjawi, R.S., Asad, J.H., Sakaj, A. et al. Lattice Green's Function for the Face Centered Cubic Lattice. Int J Theor Phys 44, 1259–1270 (2005). https://doi.org/10.1007/s10773-005-4684-z

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-005-4684-z

Keywords

Navigation