Skip to main content
Log in

Novel scaling behavior of directed polymers: Disorder distribution with long tails

  • Short Communications
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorderε is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP(ε) ∼ 1/|ε|1+μ, whereμ>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends onμ in a continuous fashion.

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.

Institutional subscriptions

References

  1. M. Kardar and Y.-C. Zhang,Phys. Rev. Lett. 58:2087 (1987).

    Google Scholar 

  2. D. Forster, D. R. Nelson, and M. J. Stephen,Phys. Rev. A 16:732 (1977).

    Google Scholar 

  3. D. A. Huse, C. L. Henley, and D. S. Fisher,Phys. Rev. Lett. 55:2924 (1985).

    Google Scholar 

  4. M. Kardar, G. Parisi, and Y.-C. Zhang,Phys. Rev. Lett. 56:889 (1986).

    Google Scholar 

  5. B. Derrida and H. Spohn,J. Physique 51:817 (1988).

    Google Scholar 

  6. J. Cook and B. Derrida,J. Stat. Phys. 57:89 (1989).

    Google Scholar 

  7. G. Parisi,J. Physique 51:1595 (1990).

    Google Scholar 

  8. M. Mezard,J. Physique 51:1831 (1990).

    Google Scholar 

  9. Y.-C. Zhang,Phys. Rev. Lett. 59:2125 (1987); and unpublished (1990).

    Google Scholar 

  10. B. Derrida and O. Golinelli,Phys. Rev. A 41:4160 (1990).

    Google Scholar 

  11. F. Guerra, private communications.

  12. E. Medina, T. Hwa, M. Kardar, and Y.-C. Zhang,Phys. Rev. A 39:3053 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bettolo Marconi, U.M., Zhang, YC. Novel scaling behavior of directed polymers: Disorder distribution with long tails. J Stat Phys 61, 885–889 (1990). https://doi.org/10.1007/BF01027307

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01027307

Key words

Navigation