Skip to main content
SpringerLink
Log in

A Theory on Flat Histogram Monte Carlo Algorithms

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

Abstract

The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the multicanonical and Wang-Landau algorithms.

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.A. Berg and T. Neuhaus, Phys. Lett. B. 267:291 (1991); Phys. Rev. Lett. 68:9 (1992); B.A. Berg and T. Celik, Phys. Rev. Lett. 69:2292 (1992).

  2. F. Wang and D.P. Landau, Phys. Rev. Lett. 86:2050 (2001); Phys. Rev. E. 64:56101 (2001).

    Google Scholar 

  3. U.H.E. Hansmann and Y. Okamoto, Journal of Computational Chemistry 18:920 (1997).

    Google Scholar 

  4. N. Rathore and J.J. de Pablo, Journal of Chemical Physics 116:7225 (2002).

    Google Scholar 

  5. R. Faller and J.J. de Pablo, Journal of Chemical Physics 119:4405 (2003).

    Google Scholar 

  6. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21:1087 (1953); W.K. Hastings, Biometrika 57:97 (1970).

    Google Scholar 

  7. B. Hesselbo and R. B. Stinchcombe, Phys. Rev. Lett. 74:2151 (1995).

    Google Scholar 

  8. F. Liang, Phys. Rev. E 69:66701 (2004).

    Google Scholar 

  9. F. Liang, unpublished.

  10. H. Robbins and S. Monro, Ann. Math. Stat. 22:400 (1951).

  11. J. R. Blum, Ann. Math. Stat. 25:737 (1954).

    Google Scholar 

  12. A. Benveniste, M. Métivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations. New York: Springer-Verlag (1990).

  13. B. A. Berg, in Monte Carlo and Quasi-Monte Carlo Methods 2000, eds. K. T. Fang, F. J. Hickernell, and H. Niederreiter, New York: Springer, pp. 168 (2000).

  14. C. Zhou and R. N. Bhatt, cond-mat/0306711 (2003).

  15. Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90:035701 (2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Texas A&M University, College Station, TX, 77843-3143, USA

    Faming Liang

Authors
  1. Faming Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Faming Liang.

Additional information

PACS number: 02.70.Tt, 02.50.Ng

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liang, F. A Theory on Flat Histogram Monte Carlo Algorithms. J Stat Phys 122, 511–529 (2006). https://doi.org/10.1007/s10955-005-8016-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-005-8016-8

Key Words

Search

Navigation