Skip to main content
SpringerLink
Log in

Single-cluster Monte Carlo dynamics for the Ising model

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

Abstract

We present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. In general, it is more efficient than Swendsen-Wang dynamics ford>2, giving zero critical slowing down in the upper critical dimension. Monte Carlo simulations give dynamical critical exponentsz w=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withz w=0 ind=4 and mean-field theory. We present scaling arguments which indicate that the Wolff mechanism for decorrelation differs substantially from Swendsen-Wang despite the apparent similarities of the two methods.

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. R. Swendsen and J. S. Wang,Phys. Rev. Lett. 58:86 (1987).

    Google Scholar 

  2. C. M. Fortuin and P. W. Kasteleyn,Physica 57:536 (1972).

    Google Scholar 

  3. A. Coniglio and W. Klein,J. Phys. A 13:2775 (1980).

    Google Scholar 

  4. F. Niedermayer,Phys. Rev. Lett. 61:2026 (1988).

    Google Scholar 

  5. R. G. Edwards and A. D. Sokal,Phys. Rev. D 38:2009 (1988); A. Sokal, Monte Carlo methods in statistical mechanics: Foundations and new algorithms, Lecture Notes.

    Google Scholar 

  6. R. Brower and P. Tamayo,Phys. Rev. Lett. 62:1087 (1989).

    Google Scholar 

  7. T. Ray, P. Tamayo, and W. Klein,Phys. Rev. A 39:5949 (1989).

    Google Scholar 

  8. P. C. Hohenberg and B. Halperin,Rev. Mod. Phys. 49:435 (1977).

    Google Scholar 

  9. W. Klein, T. Ray, and P. Tamayo,Phys. Rev. Lett. 62:163 (1989).

    Google Scholar 

  10. U. Wolff,Phys. Rev. Lett. 62:361 (1989).

    Google Scholar 

  11. P. L. Leath,Phys. Rev. B 14:5046 (1976).

    Google Scholar 

  12. K. Binder, ed.,Monte Carlo Methods in Statistical Physics (Springer-Verlag, 1979).

  13. H. Gould and J. Tobochnik,Computer Simulation Methods (Addison-Wesley, 1988).

  14. E. Stoll, K. Binder, and T. Schneider,Phys. Rev. B 8:3266 (1973).

    Google Scholar 

  15. S. Tang and D. P. Landau,Phys. Rev. B 36:567 (1987).

    Google Scholar 

  16. T. Ray and W. Klein,J. Stat. Phys. 53:773 (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department and Center for Polymer Studies, Boston University, Boston, Massachusetts

    P. Tamayo

  2. Department of Electrical, Computer and Systems Engineering and Physics Department, Boston University, Boston, Massachusetts

    R. C. Brower

  3. Physics Department and Center for Polymer Studies, Boston University, Boston, Massachusetts

    W. Klein

Authors
  1. P. Tamayo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. C. Brower
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Klein
    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

Tamayo, P., Brower, R.C. & Klein, W. Single-cluster Monte Carlo dynamics for the Ising model. J Stat Phys 58, 1083–1094 (1990). https://doi.org/10.1007/BF01026564

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01026564

Key words

Search

Navigation