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Optimized monte carlo methods

  • Enzo Marinari
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 501)

Abstract

I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, such as Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. Reweighted data analysis and multihistogramming are also discussed. I introduce simulated tempering, and, as an example, its application to the random field Ising model. I illustrate parallel tempering, and discuss some crucial technical details such as thermalization and volume scaling. I give a general perspective by discussing umbrella methods and the multicanonical approach.

Keywords

Partition Function Wilson Loop Ising Model Lattice Gauge Theory Complex Zero 
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.

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References

  1. [1]
    Falcioni, M., Marinari, E., Paciello, M. L., Parisi, G., Taglienti, B., Phys. Lett. 108B 331 (1982).ADSGoogle Scholar
  2. [2]
    Marinari, E., Nucl. Phys. B 235 123 (1984).CrossRefADSMathSciNetGoogle Scholar
  3. [3]
    Salsburg, Z., Jackson, J. D., Fickett, W., Wood, W. W., J. Chem. Phys. 30 65 (1959).CrossRefADSGoogle Scholar
  4. [4]
    Chestnut, D., Salsburg, Z., J. Chem. Phys. 38 2861 (1963).CrossRefADSGoogle Scholar
  5. [5]
    Mc Donald, I., Singer, K., J. Chem. Phys. 47 4766 (1967).CrossRefADSGoogle Scholar
  6. [6]
    Ferrenberg, A., Swendsen, R., Phys. Rev. Lett. 61 2635 (1988).CrossRefADSGoogle Scholar
  7. [7]
    Ferrenberg, A., Swendsen, R., Phys. Rev. Lett. 63 1195 (1989).CrossRefADSGoogle Scholar
  8. [8]
    Itzykson, C., Pearson, R. B., Zuber, J.-B., Nucl. Phys. B 220 415 (1983).CrossRefADSMathSciNetGoogle Scholar
  9. [9]
    Pearson, R. B., Phys. Rev. B 26 6285 (1982).ADSMathSciNetGoogle Scholar
  10. [10]
    Le Guillou, J. C., Zinn-Justin, Phys. Rev. B 21 3976 (1980).ADSGoogle Scholar
  11. [11]
    Bhanot, G., et al., Phys. Rev. Lett. 59 803 (1987).CrossRefADSGoogle Scholar
  12. [12]
    Rothe, H. J., Lattice Gauge Theory: An Introduction. (World Scientific, Singapore, 1992).zbMATHGoogle Scholar
  13. [13]
    Montvay, I., Münster, G., Quantum Fields on a Lattice. (Cambridge University Press, Cambridge UK, 1994).CrossRefGoogle Scholar
  14. [14]
    Kogut, J., Rev. Mod. Phys. 51, 659 (1979).CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    Parisi, G., A Short Introduction to Numerical Simulations of Lattice Gauge Theories. In Critical Phenomena, Random Systems, Gauge Theories, edited by K. Osterwalder and R. Stora, proceedings of Les Houches, Session XLIII, 1984 (Elsevier, Amsterdam, 1986).Google Scholar
  16. [16]
    Marinari, E., Parisi, G., Europhys. Lett. 19 451 (1992).ADSCrossRefGoogle Scholar
  17. [17]
    Fernandez, L. A., Marinari, E., Ruiz-Lorenzo, J., J. Phys. I (France) 5 1247 (1995).CrossRefGoogle Scholar
  18. [18]
    Coluzzi, B., J. Phys. A (Math. Gen.) 28 747 (1995).zbMATHCrossRefADSGoogle Scholar
  19. [19]
    Vicari, E., Phys. Lett. B 309 139 (1993).ADSGoogle Scholar
  20. [20]
    Kerler, W., Rehberg P., Simulated Tempering Approach to Spin Glass Simulations. (cond-mat/9402049).Google Scholar
  21. [21]
    Caracciolo, S., Pelissetto, A., Sokal, A. D. (1994). Unpublished note.Google Scholar
  22. [22]
    Tesi, M. C., Janse van Rensburg, E. J., E. Orlandini E., Whillington, S. G., Monte Carlo Study of the Interacting Self-Avoiding Walk Model in Three Dimensions. Oxford preprint OUTP-95-06S, J. Stat. Phys. (1995).Google Scholar
  23. [23]
    Geyer, J., Thompson, E. A., University of Minnesota preprint, 1994.Google Scholar
  24. [24]
    Hukushima, K., Takayama H., Nemoto, K., Application of an Extended Ensemble Method to Spin Glasses. Int. J. Mod. Phys. C (1995).Google Scholar
  25. [25]
    Hukushima, K., Nemoto, K., Exchange Monte Carlo Method and Application to Spin Glass Simulations. (cond-mat/9512035).Google Scholar
  26. [26]
    Krauth, W., (1996). Contribution to this volume.Google Scholar
  27. [27]
    Torrie, G. M., Valleau, J. P., J. Comp. Phys. 23 187 (1977).CrossRefADSGoogle Scholar
  28. [28]
    Torrie, G. M., Valleau, J. P., Chem. Phys. 66 1402 (1977).CrossRefADSGoogle Scholar
  29. [29]
    Graham, J. P., Valleau, J. P., Chem. Phys. 94 7894 (1990).CrossRefGoogle Scholar
  30. [30]
    Valleau, J. P., In Proceedings of the International Symposium on Ludwig Boltzmann, edited by G. Battimelli, M. G. Ianniello and O. Kreiten, (1993).Google Scholar
  31. [31]
    Berg, B. A., Neuhaus, T., Phys. Lett. B 267 249 (1991).ADSGoogle Scholar
  32. [32]
    Berg, B. A., Neuhaus, T., Phys. Rev. Lett. 68 9 (1992).CrossRefADSGoogle Scholar
  33. [33]
    Berg B. A., Celik, T., Rev. Lett. 69 2292 (1992)CrossRefADSGoogle Scholar
  34. [34]
    Berg B. A., Celik, T., Hansmann, U., Europhys. Lett. 22 63 (1993).ADSCrossRefGoogle Scholar
  35. [35]
    Kerler, W., Weber, A., Phys. Rev. B47 11563 (1993).ADSGoogle Scholar
  36. [36]
    Kondor, I., J. Phys. A22 L163 (1989).Google Scholar
  37. [37]
    Kondor, I., Végsö, A., J. Phys. A26 L641 (1993).Google Scholar
  38. [38]
    Ritort, F., Chaos in Short Range Spin Glasses. (cond-mat/9307065).Google Scholar
  39. [39]
    Marinari, E., Parisi, G., Ruiz-Lorenzo, J., (1996). In preparation.Google Scholar
  40. [40]
    Iori, G., Marinari, E., Parisi, G., (1996). In preparation.Google Scholar
  41. [41]
    Iori, G., Marinari, E., Parisi, G., J. Phys. A24 5349 (1991).ADSGoogle Scholar
  42. [42]
    Hansmann, U. H. E., Okamoto, Y., J. Comp. Chem. 14 1333 (1993).CrossRefGoogle Scholar
  43. [43]
    Rose, T., Coddington, P. D., Marinari, E., Evaluation of Simulated Tempering for Optimization Problems. NPAC preprint (Syracuse, NY, USA, 1992), unpublished, available at: ftp://ftp.npac.syr.edu/pub/projects/reu/reu92/papers/rose.ps.Google Scholar
  44. [44]
    Shore, M., Coddington, P. D., Fox, G. C., Marinari, E., A New Automatic Simulated Annealing-Type Global Optimization Scheme. NPAC preprint (Syracuse, NY, USA, 1993), unpublished, available at: ftp://ftp.npac.syr.edu/pub/projects/reu/reu93/papers/Shore.ps.Z.Google Scholar
  45. [45]
    Mézard, M., Parisi, G., Virasoro, M. A., Spin Glass Theory and Beyond. (World Scientific, Singapore, 1987).zbMATHGoogle Scholar
  46. [46]
    Marinari, E., Parisi, G., Ritort, F., Ruiz-Lorenzo, J., Phys. Rev. Lett. 76 843 (1995).CrossRefADSGoogle Scholar
  47. [47]
    Bhatt, R. N., Young, A. P., J. Magn. Matter 54 191 (1986).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Enzo Marinari
    • 1
  1. 1.Dipartimento di FisicaUniversità di CagliariCagliariItaly

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