Skip to main content
SpringerLink
Log in

Statistics of self-avoiding walks on random lattices

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The statistics of directed self-avoiding walks (SAWs) on randomly bond diluted square lattices have been solved exactly and a computer simulation study of the statistics of ordinary SAWs on diluted square lattices has also been performed. The configurational averaging has been performed here over the logarithms of the distribution functions. We find that the critical behaviour remains unchanged below a certain dilution concentrationp *, dependent on the length of the chains considered (p *=0 forN→∞), and a crossover to a higher order critical behaviour occurs beyond that point.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hiley, B.J., Finney, J.L., Burke, T.: J. Phys. A Math. Gen.10, 197 (1977)

    Google Scholar 

  2. Chakrabarti, B.K., Kertesz, J.: Z. Phys. B — Condensed Matter44, 821 (1981)

    Google Scholar 

  3. Kremer, K.: Z. Phys. B — Condensed Matter45, 149 (1981)

    Google Scholar 

  4. Derrida, B.: J. Phys. A Math. Gen.15, L119 (1982)

    Google Scholar 

  5. Harris, A.B.: Z. Phys. B — Condensed Matter49, 347 (1983)

    Google Scholar 

  6. Roy, A.K., Chakrabarti, B.K.: Phys. Lett. A91, 393 (1982)

    Google Scholar 

  7. Chakrabarti, B.K., Bhadra, K., Roy, A.K., Karmakar, S.N.: Phys. Lett. A93, 434 (1983)

    Google Scholar 

  8. Rexakis, J., Argyrakis, P.: Phys. Rev. B28, 5323 (1983)

    Google Scholar 

  9. Kim, Y.: J. Phys. C: Solid State Phys.16, 1345 (1983)

    Google Scholar 

  10. de Gennes, P.G.: Scaling concepts in polymer physics. Ithaca, New York: Cornell University Press 1979

    Google Scholar 

  11. Harris, A.B.: J. Phys. C: Solid State Phys.7, 1671 (1974)

    Google Scholar 

  12. Lubensky, T.C.: The Ill-condensed matter. Les Houches Summer Session XXXI. Amsterdam: North. Holland 1979

    Google Scholar 

  13. Derrida, B., Hilhorst, H.J. J. Phys. C: Solid State Phys.14, L539 (1981)

    Google Scholar 

  14. Fisher, M.E., Sykes, M.F.: Phys. Rev.114, 45 (1959)

    Google Scholar 

  15. Chakrabarti, B.K., Manna, S.S.: J. Phys. A: Math. Gen16, L113 (1983)

    Google Scholar 

  16. Szpilka, A.M.: J. Phys. A: Math. Gen.16, 2883 (1983)

    Google Scholar 

  17. Blote, H.W.J., Hilhorst, H.J.: Lab. Tech. Naturkunde, Delft. Prepritn (1983)

  18. Redner, S., Majid, I.: J. Phys. A: Math. Gen.16, L307 (1983)

    Google Scholar 

  19. Cardy, J.L.: J. Phys. A: Math. Gen.16, L355 (1983)

    Google Scholar 

  20. Riedel, E., Wegner, F.: Z. Phys.225, 195 (1969)

    Google Scholar 

  21. Martin, J.L., Sykes, M.F., Hioe, F.T.: J. Chem. Phys.46, 3478 (1967)

    Google Scholar 

  22. Nienhuis, B.: Phys. Rev. Lett.49, 1062 (1982)

    Google Scholar 

Download references

Author information

Author notes

  1. A. K. Roy

    Present address: Physics Department, Santipur College, 741404, Nadia, India

Authors and Affiliations

  1. Saha Institute of Nuclear Physics, 92 A.P.C. Road, 700009, Calcutta, India

    A. K. Roy & B. K. Chakrabarti

Authors
  1. A. K. Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. K. Chakrabarti
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roy, A.K., Chakrabarti, B.K. Statistics of self-avoiding walks on random lattices. Z. Physik B - Condensed Matter 55, 131–136 (1984). https://doi.org/10.1007/BF01420564

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420564

Keywords

Search

Navigation