Zeitschrift für Physik B Condensed Matter

, Volume 87, Issue 2, pp 257–264 | Cite as

Density of states, level-statistics and localization of fractons in 2- and 3-dimensional disordered systems

  • P. Argyrakis
  • S. N. Evangelou
  • K. Magoutis
Original Contributions


We calculate by the Lanczos method the density of spin wave states, and its fluctuation properties on the infinite percolating cluster of a randomly site-dilute Heisenberg ferromagnet. Our results demonstrate that the averaged density follows the fracton laws with spectral dimension valuesd s =1.32 andd s =1.30 in two and three dimensions, respectively, and is smooth at the magnon-fracton crossover. Similar laws are also shown in the case of continuous disorder on the bonds of the clusters. The density fluctuations are studied via the nearest energylevel-spacing distribution functionP(S), which is shown to obey the Wigner surmise with level-repulsion far from the percolation thresholdp c and an almost Poisson law with uncorrelated spectrum atp c . The localization properties of excitations are investigated by considering the density of states fluctuations and also via the participation ratio of the eigenvector amplitudes. It is seen that the fracton states are sharply localized. Our results are further discussed in connection to previous theories and numerical data.


Neural Network Spectral Dimension Numerical Data Percolate Localization Property 
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  1. 1.
    Mandelbrot, B.B.: The fractal geometry of nature. San Francisco: Freeman 1982Google Scholar
  2. 2.
    Stauffer, D.: Introduction to percolation theory. London: Taylor and Francis 1985Google Scholar
  3. 3.
    Havlin, S., ben-Avraham, D.: Adv. Phys.36, 695 (1987)Google Scholar
  4. 4.
    Alexander, S., Orbach, R.: J. Phys. (Paris) Lett.43, L625 (1982)Google Scholar
  5. 5.
    Stinchcombe, R.B.: In: Scaling phenomena in disordered systems. Pynn, R., Skjeltorp, A. (eds.), p. 13. New York: Plenum Press 1985Google Scholar
  6. 6.
    Evangelou, S.N.: Phys. Rev. B33, 3602 (1986)Google Scholar
  7. 7.
    Evangelou, S.N., Papanicolaou, N., Economou, E.N.: Phys. Rev. B43, 11171 (1991)Google Scholar
  8. 8.
    Aharony, A., Alexander, S., Entin-Wohlman, O., Orbach, R.: Phys. Rev. B31, 2565 (1985)Google Scholar
  9. 9.
    Orbach, R.: Science231, 814 (1986)Google Scholar
  10. 10.
    Alexander, S., Laermans, C., Orbach, R., Rosenberg, H.M.: Phys. Rev. B28, 4615 (1983)Google Scholar
  11. 11.
    Pfeifer, P., Order, M.: In: The fractal approach to hetergenous chemistry. Avnir, D. (ed.), pp. 11–43). New York: Wiley 1989Google Scholar
  12. 12.
    Rammal, R., Toulouse, G.: J. Phys. (Paris) Lett.44, 13 (1983)Google Scholar
  13. 13.
    Kirpatrick, S., Eggarter, T.P.: Phys. Rev. B6, 3598 (1972)Google Scholar
  14. 14.
    Levy, Y.E., Souillard, B.: Europhys. Lett.4, 233 (1987)Google Scholar
  15. 15.
    Porter, C.E.: Statistical theories of spectra: fluctuations. New York: Academic Press 1965Google Scholar
  16. 16.
    Altshuler, B.L.: Proceedings of the 18th International Conference on Low Temperature Physics. Jpn. J. Appl. Phys. Suppl.26, 1938 (1987)Google Scholar
  17. 17.
    Parlett, B.N., Reid, J.K.: AERE Harwell Report No CSS83 (1980); also see Cullum, J.K., Willoughby, R.K.: Lanczos algorithms for large symmetric eigenvalue problems. Boston, Basel, Stuttgart: Birkhauser 1985Google Scholar
  18. 18.
    Hoshen, J., Kopelman, R.: Phys. Rev. B14, 3428 (1976)Google Scholar
  19. 19.
    Argyrakis, P.: In: Structure and dynamics of molecular systems. Daudel, R., Korb, J.P., Lemaistre, J.P., Maruani, J. (eds.), pp. 209. Dordrecht: D. Reidel 1986Google Scholar
  20. 20.
    Evangelou, S.N.: Phys. Rev. B27, 1397 (1983)Google Scholar
  21. 21.
    Lewis, S.J., O'Brien, M.C.M.: J. Phys. B18, 4487 (1985)Google Scholar
  22. 22.
    O'Brien, M.C.M., Evangelou, S.N.: J. Phys. C6, 3598 (1980)Google Scholar
  23. 23.
    Altshuler, B.L., Zharekeshev, I.Kh., Kotochigova, S.A., Shklovskii, B.I.: Sov. Phys. JETP67, 625 (1988)Google Scholar
  24. 24.
    Bohigas, O., Giannoni, M.J.: Mathematical and computational methods in nuclear physics. Dehesa, J.S., Gomea, J.M., Polls, A. (eds.). In: Lecture Notes in Physics, p. 1. Berlin, Heidelberg, New York: Springer 1984Google Scholar
  25. 25.
    Thouless, D.J.: Phys. Rep.13, 93 (1974)Google Scholar
  26. 26.
    Nakayama, T., Yakubo, K., Orbach, R.: J. Phys. Soc. Jpn.58, 1891 (1989)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • P. Argyrakis
    • 1
  • S. N. Evangelou
    • 2
  • K. Magoutis
    • 1
  1. 1.Department of Physics 313-1University of ThessalonikiThessalonikiGreece
  2. 2.Department of PhysicsUniversity of IoanninaIoanninaGreece

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