Skip to main content

Monte Carlo Simulation of Dilute Systems and of Two-Dimensional Systems

  • Chapter

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 50))

Abstract

These lectures are concerned with several types of systems: ferromagnets diluted with impurities; quasi-twodimensional (2d) magnets; monolayers of adsorb ate atoms at surfaces and their registered structures. Emphasis will be on static properties, as studied by Monte Carlo (MC) methods. It will be shown how such numerical results elucidate theoretical questions as well as experiments. Of course, only a few examples mainly selected from the work of the author’s group can be given here;a detailed bibliography on other studies, as well as a description of the theory of the MC method and its technical aspects is found in a recent book /1/.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Binder (ed.) Monte Carlo Methods in Statistical Physics.

    Google Scholar 

  2. Springer, Berlin 1979.

    Google Scholar 

  3. V. Wildpaner et al., J. Phys. Chem. Sol. 34, 925 (1973).

    Article  ADS  Google Scholar 

  4. K. Binder, W. Kinzel and D. Stauffer, to be published.

    Google Scholar 

  5. H. Maletta and P. Convert, Phys. Rev. Lett. 42, 108 (1979).

    Article  ADS  Google Scholar 

  6. See e.g. W.Y. Ching and D.L. Huber, Phys. Rev. B13, 2962 (1976).

    ADS  Google Scholar 

  7. D.P. Landau, Physica B86–88, 731 (1979)

    Google Scholar 

  8. C. Jayaprakash et al., Phys. Rev. B17, 2244 (1978).

    ADS  Google Scholar 

  9. H.A. Algra et al., Phys. Rev. Lett. 42, 606 (1979).

    Article  ADS  Google Scholar 

  10. G.S. Rushbrooke, in Critical Phenomena in Alloys, Magnets, and Superconductors (eds.: R.E. Mills, E. Ascher and R.I. Jaffee), p. 155 (McGraw Hill, New York 1971).

    Google Scholar 

  11. H. Dvey-Aharon and M. Fibich, Phys. Rev. B18, 3491 (1978).

    ADS  Google Scholar 

  12. See also lectures on Spin Glasses by K. Binder in this book.

    Google Scholar 

  13. R.J. Birgeneau et al., Phys. Rev. Lett. 37, 940 (1976). See also lectures by R. Cowley in this book.

    Article  ADS  Google Scholar 

  14. R.E. Watson et al., Phys. Rev. B2:, 684 (1970).

    ADS  Google Scholar 

  15. C. Kawabata and K. Binder, Solid State Comm. 22, 705 (1977).

    Article  ADS  Google Scholar 

  16. D.P. Landau, Phys. Rev. B13, 2997 (1976), and references therein.

    ADS  Google Scholar 

  17. K. Binder and D.P. Landau, Phys. Rev. B13, 1140 (1976).

    ADS  Google Scholar 

  18. R.J. Birgeneau et al., Phys. Rev. B8, 1736 (1971);

    ADS  Google Scholar 

  19. R.J. Birgeneau et al., Phys. Rev. B16, 280 (1977).

    ADS  Google Scholar 

  20. D.R. Nelson and R.A. Pelcovits, Phys. Rev. B16, 2191 (1977).

    ADS  Google Scholar 

  21. H.E. Stanley and T.A. Kaplan, Phys. Rev. Lett. 17, 913 (1966).

    Article  MathSciNet  ADS  Google Scholar 

  22. S. Krinsky and D. Mukamel, Phys. Rev. B16, 2313 (1977).

    ADS  Google Scholar 

  23. D.P. Landau, preprint.

    Google Scholar 

  24. K. Binder and D.P. Landau, preprint.

    Google Scholar 

  25. J.V. Jose et al., Phys. Rev. B16, 1277 (1977).

    Google Scholar 

  26. For a general discussion of these concepts see E. Domany and E.K. Riedel, J. Appl. Phys. 49, 1315 (1978).

    Article  ADS  Google Scholar 

  27. E. Domany et al., Phys. Rev. B12, 5025 (1975).

    ADS  Google Scholar 

  28. J.G. Dash, Films on Solid. Surfaces (Academic Press, New York 1975);

    Google Scholar 

  29. J.G. Dash, Phys. Repts. 38C, 177 (1978).

    Article  ADS  Google Scholar 

  30. G.A. Somorjai, Surf. Sci. 34, 156 (1973);

    Article  ADS  Google Scholar 

  31. K. Masuda, J. Phys. (Paris) 40, 299 (1979).

    Article  Google Scholar 

  32. K. Binder, in Trends in Physics, Proc. IV Gen. EPS Conf., York 1978, in press.

    Google Scholar 

  33. L.K. Runnels, in Phase Transitions and Critical Phenomena Vol, 2 (C. Domb and”M. S.Green, eds.) Chap 8(Academic Press, New York 1972).

    Google Scholar 

  34. H.E. Stanley, J. Phys. A10, L211 (1977) and references therein.

    Google Scholar 

  35. D. Stauffer, Z. Phys. B25, 391 (1975).

    ADS  Google Scholar 

  36. D.P. Landau, Phys. Rev. Lett. 28, 449 (1972).

    Article  ADS  Google Scholar 

  37. K. Binder and D.P. Landau, Surf. Sci. 61, 577 (1976).

    Google Scholar 

  38. T.M. Lu et al., Phys. Rev. Lett. 39, 411 (1977).

    Article  ADS  Google Scholar 

  39. W.Y. Ching et al., to be published.

    Google Scholar 

  40. B. Mihura and D.P. Landau,. Phys. Rev. Lett. 38, 977 (1976).

    Article  ADS  Google Scholar 

  41. S. Alexander, Phys. Lett. 54A, 353 (1975).

    ADS  Google Scholar 

  42. R.B. Potts, Proc. Cambridge Phil. Soc. 48, 106 (1952).

    MathSciNet  MATH  Google Scholar 

  43. J.P. Straley and M.E. Fisher, J. Phys. A6, 1310 (1973).

    ADS  Google Scholar 

  44. T. de Neef and Ï.G. Enting, J. Phys. A10, 801 (1977).

    ADS  Google Scholar 

  45. M. Bretz, Phys. Rev. Lett. 38, 501 (1977).

    Article  ADS  Google Scholar 

  46. R.J. Swendsen, preprint, and references contained in /1/.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Plenum Press, New York

About this chapter

Cite this chapter

Binder, K. (1980). Monte Carlo Simulation of Dilute Systems and of Two-Dimensional Systems. In: Riste, T. (eds) Ordering in Strongly Fluctuating Condensed Matter Systems. NATO Advanced Study Institutes Series, vol 50. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3626-6_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-3626-6_25

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-3628-0

  • Online ISBN: 978-1-4684-3626-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics