Skip to main content
SpringerLink
Log in

Transition from the Compact to the Dense Phase of Two-Dimensional Polymers

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

Abstract

We present a unifying picture of the compact, dense, and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute cases. In particular, we show that violations of the fully packing constraint in the compact phase can be interpreted as magnetic screening in the associated Coulomb gas, which induces a flow to either the dense or the dilute phase. When more than one flavor of polymers is present the flow away from the compact phase leads to a decoupling of the flavors, and the central charge decreases by an integer. If charge asymmetry develops, the polymer flavors may independently flow to either of the two noncompact phases.

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. B. Nienhuis, in Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic, London, 1987), Vol. 11.

    Google Scholar 

  2. H. W. J. Blöte and B. Nienhuis, Phys. Rev. Lett. 72:1372 (1994).

    Google Scholar 

  3. M. T. Batchelor, J. Suzuki, and C. M. Yung, Phys. Rev. Lett. 73:2646 (1994).

    Google Scholar 

  4. J. Kondev, J. de Gier, and B. Nienhuis, J. Phys. A 29:6489 (1996).

    Google Scholar 

  5. M. T. Batchelor, H. W. J. Blöte, B. Nienhuis, and C. M. Yang, J. Phys. A 29:L399 (1996).

    Google Scholar 

  6. J. L. Jacobsen and J. Kondev, Nucl. Phys. B 532:635 (1998).

    Google Scholar 

  7. B. Duplantier and H. Saleur, Nucl. Phys. B 290:291 (1987).

    Google Scholar 

  8. H. S. Chan and K. A. Dill, Macromolecules 22:4559 (1989).

    Google Scholar 

  9. H. Orland, C. Itzykson, and C. de Dominicis, J. Phys. (Paris) 46:L353 (1985).

    Google Scholar 

  10. H. W. J. Blöte and B. Nienhuis, J. Phys. A 22:1415 (1989).

    Google Scholar 

  11. J. Kondev, Phys. Rev. Lett. 78:4320 (1997).

    Google Scholar 

  12. J. Kondev and C. L. Henley, Phys. Rev. B 52:6628 (1995).

    Google Scholar 

  13. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6:1181 (1973).

    Google Scholar 

  14. J. Kondev and C. L. Henley, Nucl. Phys. B 464:504 (1996).

    Google Scholar 

  15. Vl. S. Dotsenko and V. A. Fateev, Nucl. Phys. B 240:312 (1984); ibid. 251:691 (1985).

    Google Scholar 

  16. J. Kondev, unpublished.

  17. J. Fuchs, Affine Lie Algebras and Quantum Groups (Cambridge University Press, Cambridge, 1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Statistique (Laboratoire associé aux Universités Paris 6, Paris 7 et au CNRS), Ecole Normale Supérieure, 75231, Paris Cedex 05, France

    Jesper Lykke Jacobsen

  2. Institute for Advanced Study, Princeton, New Jersey, 08540

    Jané Kondev

  3. Department of Physics, Princeton University, Princeton, New Jersey, 08540

    Jané Kondev

Authors
  1. Jesper Lykke Jacobsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jané Kondev
    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

Jacobsen, J.L., Kondev, J. Transition from the Compact to the Dense Phase of Two-Dimensional Polymers. Journal of Statistical Physics 96, 21–48 (1999). https://doi.org/10.1023/A:1004512230458

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004512230458

Search

Navigation