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Numerical studies of spin glasses

  • I. Spin Glasses
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Part of the book series: Lecture Notes in Physics ((LNP,volume 275))

Abstract

We survey the progress in numerical studies of spin glasses since the first Heidelberg Colloquium, and discuss the resulting advances in our understanding of the field. A clear case can be made for the importance of using multiple methods of attack for the same problem. Combination methods, e.g. finite size scaling and Monte Carlo simulations, which we cover in some detail, are found to be particularly useful. Some remaining outstanding issues are raised, and directions for future work suggested.

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References

  1. G. Toulouse, in Disordered Systems and Localization, C. Castellani, C. DiCastro and L. Peliti eds. (Springer Lecture Notes in Physics, Vol. 149, 1981), p. 166.

    Google Scholar 

  2. For a review, see K. Binder and A. P. Young, Reviews of Modern Physics 58 (Oct. 1986).

    Google Scholar 

  3. See e.g. articles by I. Morgenstern and A. P. Young in the Heidelberg Colloquium on Spin Glasses, J. L. van Hemmen and I. Morgenstern eds., (Springer-Verlag, 1983).

    Google Scholar 

  4. A. Ogielski, these proceedings.

    Google Scholar 

  5. S. F. Edwards and P. W. Anderson, J. Phys. F5, 965 (1975).

    Article  ADS  Google Scholar 

  6. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975).

    Article  ADS  Google Scholar 

  7. K. Binder, Z. Phys. B48, 319 (1982).

    Article  ADS  Google Scholar 

  8. A. Ogielski, Phys. Rev. B32, 7384 (1985).

    ADS  Google Scholar 

  9. J. D. Reger and A. Zippelius, Phys. Rev. B31, 5900 (1985).

    ADS  Google Scholar 

  10. J. R. L. deAlmeida and D. J.Thouless, J. Phys. All, 983 (1978).

    Google Scholar 

  11. M. Gabay and G. Toulouse, Phys. Rev. Lett. 47, 201 (1981).

    Article  ADS  Google Scholar 

  12. G. Parisi, Phys. Rev. Lett. 43, 1754 (1979); ibid 50, 1946 (1983).

    Article  ADS  Google Scholar 

  13. I. Morgenstern and K. Binder, Phys. Rev. Lett. 43, 1615 (1979); W. Kinzel and K. Binder, Phys. Rev. Lett. 50, 1509 (1983).

    Article  ADS  Google Scholar 

  14. A. P. Young, Phys. Rev. Lett. 50, 917 (1983).

    Article  ADS  Google Scholar 

  15. I. Morgenstern and K. Binder, Z. Phys. B39, 227 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  16. R. Fisch and A. B. Harris, Phys. Rev. Lett. 38, 785 (1977).

    Article  ADS  Google Scholar 

  17. A. J. Bray and M. A. Moore, J. Phys. C12, 79 (1979); H. Sompolinsky and A. Zippelius, Phys. Rev. Lett. 50, 1294 (1983).

    ADS  Google Scholar 

  18. B. W. Southern and A. P. Young, J. Phys. C10, 2179 (1977); S. Kirkpatrick, Phys. Rev. B15, 1533 (1977).

    ADS  Google Scholar 

  19. J. Banavar and M. Cieplak, Phys. Rev. Lett. 48, 832 (1982).

    Article  ADS  Google Scholar 

  20. P. W. Anderson and C. M. Pond, Phys. Rev. Lett. 40, 903 (1978).

    Article  ADS  Google Scholar 

  21. R. E. Walstedt and L. R. Walker, Phys. Rev. Lett. 47, 1624 (1981).

    Article  ADS  Google Scholar 

  22. See e.g. M. N. Barber in Phase Transitions and Critical Phenomena C. Domb and J. Lebowitz eds., (Academic, New York, 1983) vol. 8 p. 146.

    Google Scholar 

  23. A. Ogielski and I. Morgenstern, Phys. Rev. Lett. 54, 928 (1985); J. Appl. Phys. 57, 3382 (1985).

    Article  ADS  Google Scholar 

  24. A. P. Young, J. Phys. C18, L517 (1984).

    Google Scholar 

  25. W. L. McMillan, Phys. Rev. B29, 4026 (1984); ibid B30, 476 (1984).

    ADS  Google Scholar 

  26. A. J. Bray and M. A. Moore, J. Phys. C17, L463 (1984).

    ADS  Google Scholar 

  27. R. N. Bhatt and A. P. Young, Phys. Rev. Lett. 54, 924 (1985).

    Article  ADS  Google Scholar 

  28. R. N. Bhatt and A. P. Young (preprint, 1986).

    Google Scholar 

  29. N. Sourlas, J. Physique Lett. 45, L969 (1984).

    Article  MathSciNet  Google Scholar 

  30. J. M. Kosterlitz and D. J. Thouless, J. Phys. C6, 1181 (1973); J. M. Kosterlitz, J. Phys. C7, 1046 (1974).

    ADS  Google Scholar 

  31. D. S. Fisher and D. A. Huse, Phys. Rev. Lett. 56, 1601 (1986); preprint (1986).

    Article  ADS  Google Scholar 

  32. R. N. Bhatt and A. P. Young (in preparation).

    Google Scholar 

  33. W. L. McMillan, Phys. Rev. B28, 5216 (1983).

    ADS  Google Scholar 

  34. H. F. Cheung and W. L. McMillan, J. Phys. C16, 7027 (1983).

    ADS  Google Scholar 

  35. H. F. Cheung and W. L. McMillan, J. Phys. C16, 7033 (1983).

    ADS  Google Scholar 

  36. D. A. Huse and I. Morgenstern, Phys. Rev. B32, 3032 (1985).

    ADS  Google Scholar 

  37. W. L. McMillan, Phys. Rev. B31, 340 (1985).

    ADS  Google Scholar 

  38. A. J. Bray and M. A. Moore, Phys. Rev. B31, 631 (1985).

    ADS  Google Scholar 

  39. R. R. P. Singh and S. Chakravarty, Phys. Rev. Lett. 57, 245 (1986); Proc. Magnetism and Magnetic Materials Conference (Baltimore, Nov. 1986).

    Article  ADS  Google Scholar 

  40. G. Kotliar, P. W. Anderson and D. L. Stein, Phys. Rev. B27, 602 (1983).

    MathSciNet  ADS  Google Scholar 

  41. See e.g., K. Binder, Z. Phys. B26, 339 (1977) and W. Y. Ching and D. L. Huber, Phys. Lett. A59, 383 (1977).

    ADS  Google Scholar 

  42. It should be noted, however, that a similar analysis led them to the conclusion of an LCD of d = 4 for the nearest neighbor Ising spin glass (see M. Cieplak and J. R. Banavar, Phys. Rev. B27, 293 (1983)), which is now believed to be erroneous.

    ADS  Google Scholar 

  43. W. L. McMillan, Phys. Rev. B31, 342 (1985).

    ADS  Google Scholar 

  44. B. W. Morris, S. G. Colborne, M. A. Moore, A. J. Bray and J. Canisius, J. Phys. C19, 1157 (1986).

    ADS  Google Scholar 

  45. J. A. Olive, A. P. Young and D. Sherrington, Phys. Rev. B (in press).

    Google Scholar 

  46. S. Jain and A. P. Young, J. Phys. C19, 3913 (1986).

    ADS  Google Scholar 

  47. A. C. D. van Enter and J. L. van Hemmen, J. Stat. Phys. 39, 1 (1985).

    Article  MATH  ADS  Google Scholar 

  48. J. Frohlich and B. Zegarlinski, Europhys. Lett. 2, 53 (1986).

    Article  ADS  Google Scholar 

  49. R. N. Bhatt and A. P. Young, J. Magn. Mag. Materials 54–57, 191 (1986).

    Article  Google Scholar 

  50. R. N. Bhatt and A. P. Young, Bull. Am. Phys. Soc. 31, 379 (1986).

    Google Scholar 

  51. A. Chakrabarti and C. Dasgupta, Phys. Rev. Lett. 56, 1404 (1986).

    Article  ADS  Google Scholar 

  52. A. J. Bray, M. A. Moore and A. P. Young, Phys. Rev. Lett. 56, 2641 (1986).

    Article  ADS  Google Scholar 

  53. C. H. Henley, Ann. Phys. (N.Y.) 156, 324, 368 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  54. G. Kotliar and H.Sompolinsky, Phys. Rev. Lett. 53, 1751 (1984).

    Article  ADS  Google Scholar 

  55. A. P. Young and R. N. Bhatt, J. Magn. Mag. Mat. 54–57, 6 (1986).

    Article  Google Scholar 

  56. P. Monod and H. Bouchiat, J. Physique Lett. 43, L45 (1982); A. P. Molozemof, Y. Imry and B. Barbara, J. Appl. Phys. 53, 7672 (1982); R. Omari, J. J. Préjean and J. Souletie, J. Physique Colloq. 44, C9-1069 (1983); P. Beauvillain, C. Chappert and J. P. Renard, J. Physique Lett. 45, L665 (1984).

    Article  Google Scholar 

  57. H. Bouchiat, J. Physique 47, 71 (1986); L. P. Levy and A. T. Ogielski, Phys. Rev. Lett. (to be published).

    Article  Google Scholar 

  58. Binder and Young (Ref. 2) have taken the conservative line that Tc = 0 in d = 3 is still within the realm of possibilities. While we agree that numerical results cannot be conclusive in this regard, the amount of evidence available makes it unlikely that de > 3; it is certainly not much larger.

    Google Scholar 

  59. I. Morgenstern, these proceedings.

    Google Scholar 

  60. I. Morgenstern, Phys. Rev. B27, 4522 (1983).

    ADS  Google Scholar 

  61. M. Mezard, G. Parisi, N. Sourlas, G. Toulouse and M. Virasoro, ibid. 52, 1156 (1984).

    ADS  Google Scholar 

  62. M. A. Moore and A. J. Bray, J. Phys. C18, L699 (1985).

    MathSciNet  ADS  Google Scholar 

  63. W. L. McMillan, J. Phys. C17, 3179 (1984).

    ADS  Google Scholar 

  64. M. A. Moore (preprint, 1986).

    Google Scholar 

  65. J. Villain (preprint, 1986).

    Google Scholar 

  66. J. Villain, in III-Condensed Matter, edited by R. Balian et al (North Holland, Amsterdam, 1979).

    Google Scholar 

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J. L. van Hemmen I. Morgenstern

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© 1987 Springer-Verlag

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Bhatt, R.N., Young, A.P. (1987). Numerical studies of spin glasses. In: van Hemmen, J.L., Morgenstern, I. (eds) Heidelberg Colloquium on Glassy Dynamics. Lecture Notes in Physics, vol 275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057518

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  • DOI: https://doi.org/10.1007/BFb0057518

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