Skip to main content
SpringerLink
Log in

The Dilute Potts Model on Random Surfaces

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

Abstract

We present a new solution of the asymmetric two-matrix model in the large-N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.

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. E. Brézin, C. Itzykson, G. Parisi, and J.-B. Zuber, Commun. Math. Phys. 59:35 (1978).

    Google Scholar 

  2. V. A. Kazakov, Mod. Phys. Lett. A 4:2125 (1989).

    Google Scholar 

  3. C. Itzykson and J.-B. Zuber, J. Math. Phys. 21:411 (1980).

    Google Scholar 

  4. H. Chandra, Amer. J. Math. 79:87 (1957).

    Google Scholar 

  5. M. L. Mehta, Comm. Math. Phys. 79:327 (1981).

    Google Scholar 

  6. S. Chadha, G. Mahoux, and M. L. Mehta, J. Phys. A 14:579 (1981).

    Google Scholar 

  7. D. V. Boulatov and V. A. Kazakov, Phys. Lett. B 186:379 (1987).

    Google Scholar 

  8. J. Alfaro, Phys. Rev. D 47:4714 (1993).

    Google Scholar 

  9. D. V. Boulatov, Mod. Phys. Lett. A 8:557 (1993).

    Google Scholar 

  10. M. Staudacher, Phys. Lett. B 305:332(1993).

    Google Scholar 

  11. P. Zinn-Justin, Commun. Math. Phys. 194:631 (1998).

    Google Scholar 

  12. V. A. Kazakov and P. Zinn-Justin, to be published in Nucl. Phys. B.

  13. E. Brézin and D. J. Gross, Phys. Lett. B 97:120 (1980).

    Google Scholar 

  14. I. Kostov, Nucl. Phys. B (Proc. Suppl.) 10A:295 (1989); D. J. Gross and M. J. Newman, Phys. Lett. B 266:291 (1991).

    Google Scholar 

  15. V. A. Kazakov, Nucl. Phys. B (Proc. Suppl.) 4:93 (1988).

    Google Scholar 

  16. J. M. Daul, preprint hep-th_9502014.

  17. V. A. Kazakov, M. Staudacher, and T. Wynter, Commun. Math. Phys. 179:235 (1996).

    Google Scholar 

  18. G. Moore, N. Seiberg, and M. Staudacher, Nucl. Phys. B 362:665 (1991).

    Google Scholar 

  19. I. Kostov, Nucl. Phys. B 376:539 (1992).

    Google Scholar 

  20. I. Kostov and M. Staudacher, Nucl. Phys. B 384:459 (1992).

    Google Scholar 

  21. K. Fukazawa, K. J. Hamada, and H. Sato, Mod. Phys. Lett. A 5-29:2431 (1990).

    Google Scholar 

  22. B. Nienhuis, A. N. Berker, E. K. Riedel, and M. Schick, Phys. Rev. Lett. 43:737 (1979).

    Google Scholar 

  23. V. A. Kazakov, Mod. Phys. Lett. A 4:1691 (1989).

    Google Scholar 

  24. G. Bonnet, preprint hep-th_9904058.

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey, 08854-8019

    P. Zinn-Justin

Authors
  1. P. Zinn-Justin
    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

Zinn-Justin, P. The Dilute Potts Model on Random Surfaces. Journal of Statistical Physics 98, 245–264 (2000). https://doi.org/10.1023/A:1018626906256

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018626906256

Search

Navigation