Histogram Techniques for Studying Phase Transitions

  • A. M. Ferrenberg
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 53)

Abstract

The use of histogram techniques to increase the efficiency of Monte Carlo computer simulations is discussed. The early history, as well as more recent refinements are presented. The power of the technique is demonstrated by Monte Carlo studies of three statistical mechanical models.

Keywords

Monte Carlo Monte Carlo Simulation Ising Model Monte Carlo Study Dime Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).ADSCrossRefGoogle Scholar
  2. 2.
    N. Metropolis, “Monte Carlo Methods in Statistical Physics”, Second Edition, K. Binder, ed., (Springer-Verlag, New York, 1986).Google Scholar
  3. 3.
    K. Binder, J. Comp. Phys. 59, 1 (1985).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    K. Binder, “Recent Trends in the Development and Application of the Monte Carlo Method”, in Reference 2.Google Scholar
  5. 5.
    R.H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    R.H. Swendsen, Phys. Rev. Lett. 42, 859 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    A.M. Ferrenberg and R.H. Swendsen, Phys. Rev. Lett., 61, 2635 (1988).ADSCrossRefGoogle Scholar
  8. 8.
    Z.W. Saisburg, J.D. Jackson, W. Fickett and W.W. Wood, J. Chem. Phys. 30, 65 (1959).ADSCrossRefGoogle Scholar
  9. 9.
    D.A. Chesnut and Z.W. Salsburg, J. Chem. Phys. 38, 2861 (1963).ADSCrossRefGoogle Scholar
  10. 10.
    R. McDonald and K. Singer, Disc. Far. Soc, 43, 400 (1967).CrossRefGoogle Scholar
  11. 11.
    A.M. Ferrenberg and R.H. Swendsen, “Optimized Monte Carlo Data Analysis”, Computers in Physics, Vol. 3, No. 5, (1989).Google Scholar
  12. 12.
    M. Falcioni, E. Marinari, M.L. Paciello, G. Parisi and B. Taglienti, Phys. Lett. 108B, 331 (1982).ADSGoogle Scholar
  13. 13.
    E. Marinari, Nucl. Phys. B235 [FS11], 1233 (1984).MathSciNetGoogle Scholar
  14. 14.
    G. Bhanot, S. Black, P. Carter and R. Salvador, Phys. Lett. B183, 331 (1987).ADSGoogle Scholar
  15. 15.
    G. Bhanot, K.M. Bitar, S. Black, P. Carter and R. Salvador, Phys. Lett. B187, 381 (1987).ADSGoogle Scholar
  16. 16.
    G. Bhanot, K.M. Bitar and R. Salvador, Phys. Lett. B188, 246 (1987).MathSciNetADSGoogle Scholar
  17. 17.
    G. Bhanot, R. Salvador, S. Black and R. Toral, Phys. Rev. Lett. 59, 803 (1987).ADSCrossRefGoogle Scholar
  18. 18.
    A.M. Ferrenberg and R.H. Swendsen, Phys. Rev. Lett., 63, 1195 (1989).ADSCrossRefGoogle Scholar
  19. 19.
    P.B. Bowen, J.L. Burke, P.G. Corsten, K.J. Crowell, K.L. Farrell, J.C. Macdonald, R.P. Macdonald, A.B. Maclsaac, S.C. Maclsaac, P.H. Poole and N. Jan, Phys. Rev. B 40, 3454 (1989).Google Scholar
  20. 20.
    N.A. Alves, B.A. Berg and R. Villanova, Phys. Rev. B 41, 383 (1990).MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    A.M. Ferrenberg and R.H. Swendsen, “Histogram Methods in Statistical Physics”, submitted to Int. Rev. Mod. Phys.Google Scholar
  22. 22.
    A.M. Ferrenberg, D.P. Landau and K. Binder, submitted to J. Stat. Phys.Google Scholar
  23. 23.
    A.M. Ferrenberg and D.P. Landau, preprint.Google Scholar
  24. 24.
    S. Wansleben, Comp. Phys. Comm. 43, 315 (1987).ADSCrossRefGoogle Scholar
  25. 25.
    J.F. Nagle, A. Yanagawa and J. Stecki, Mol. Cryst. Liq. Cryst, 37, 127 (1976).CrossRefGoogle Scholar
  26. 26.
    A.M. Ferrenberg, C. Schiff, J.G. Fetkovich and J.F. Nagle, preprint.Google Scholar
  27. 27.
    A. Rahman and F.H. Stillinger, J. Chem. Phys. 57, 4009 (1972).ADSCrossRefGoogle Scholar
  28. 28.
    K. Binder, Z. Phys. B 43, 119 (1981).CrossRefGoogle Scholar
  29. 29.
    M.E. Fisher, Proceedings of the International Summer School “Enrico Fermi” Course 51 (Academic, New York, 1971).Google Scholar
  30. 30.
    P. Peczak, A.M. Ferrenberg and D.P. Landau, preprint.Google Scholar
  31. 31.
    P. Peczak and D.P. Landau, J. Appl. Phys. 67, 5427 (1990).ADSCrossRefGoogle Scholar
  32. 32.
    J.C. LeGuillou and J. Zinn-Justin, Phys. Rev. B21, 3976 (1980); J. Phys. Lett. 46, L137 (1985).MathSciNetADSGoogle Scholar
  33. 33.
    D.S. Ritchie and M.E. Fisher, Phys. Rev. B 5, 2668 (1972).ADSCrossRefGoogle Scholar
  34. 34.
    M.P. Nightingale and H.W.J. Blöte, Phys. Rev. Lett. 60, 1562 (1988).ADSCrossRefGoogle Scholar
  35. 35.
    B.G. Nickel, Phase Transitions: Cargese 1980, M. Levy, J.-C. LeGuillou and J. Zinn-Justin, eds. (Plenum, New York, 1982).Google Scholar
  36. 36.
    A.J. Liu and M.E. Fisher, Physica A 165, 35 (1989).MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    G.S. Pawley, R.H. Swendsen, D.J. Wallace and K.G. Wilson, Phys. Rev. B 29, 4030 (1984).ADSCrossRefGoogle Scholar
  38. 38.
    H.W.J. Blöte, J. de Bruin, A. Compagner, J.H. Croockewit, Y.T.J.C. Fonk, J.R. Heringa, A. Hoogland, and A.L. van Willigen, Europhys. Lett. 10, 105 (1989).ADSCrossRefGoogle Scholar
  39. 39.
    H.W.J. Blöte, A. Compagner, J.H. Croockewit, Y.T.J.C. Fonk, J.R. Heringa, T.S. Smit, and A.L. van Willigen, Physica A161, 1 (1989).ADSGoogle Scholar
  40. 40.
    D.P. Landau, Phys. Rev. B 14, 255 (1976).ADSCrossRefGoogle Scholar
  41. 41.
    M.N. Barber, R.B. Pearson, D. Toussaint, and J.L. Richardson, Phys. Rev. B32, 1720 (1985).ADSGoogle Scholar
  42. 42.
    G. Parisi and F. Rapuano, Phys. Lett. B157, 301 (1985).MathSciNetADSGoogle Scholar
  43. 43.
    G. Bhanot, D. Duke, and R. Salvador, Phys. Rev. B 33, 7841 (1986).ADSCrossRefGoogle Scholar
  44. 44.
    S. Wansleben and D.P. Landau, J. Appl. Phys. 61, 3968 (1987) and unpublished.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • A. M. Ferrenberg
    • 1
  1. 1.Center for Simulational PhysicsThe University of GeorgiaAthensUSA

Personalised recommendations