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The spin glass transition: a comparison of Monte Carlo simulations of nearest-neighbor Ising Edwards-Anderson models with experiments

  • Theoretical Papers
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Heidelberg Colloquium on Spin Glasses

Part of the book series: Lecture Notes in Physics ((LNP,volume 192))

Abstract

Numerical studies of Ising square lattices with random bonds (Jij =±J or drawn from a gaussian distribution) are reviewed. Particular attention is paid to the temperature- and field dependence of the equilibrium magnetization M(H,T). While for a symmetric bond distribution the zero-field susceptibility trivially follows a Curies law Xo∝ T−1, the nonlinear susceptibility Xn ℓ shows a dramatic temperature-dependence, which can nearly be mistaken for a power-law divergence at a freezing temperature Tf. These findings are compared in detail with corresponding experimental data, including possible “scaling” representations. We relate this behavior to the onset of long-range Edwards-Anderson order as T→0, as measured by the correlation function gEA(rij)=[<SiSj> 2T ]av

We then discuss time-dependent quantities: the spin-spin autocorrelation function and the time-dependent Edwards-Anderson order parameter q(t), dynamic susceptibility χ(t) etc.; also the onset of irreversible behavior at critical magnetic fields Hc(t) is emphasized, and again compared to experiments. A possible explanation of this behavior in terms of the free energy barriers separating the various “valleys” in configuration space is indicated.

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References

  1. L. Néel, Ann. Geophys. l5, 99 (1949)

    Google Scholar 

  2. J.L. Tholence and R. Tournier, J. Phys. (Paris) 35, C4–229 (1974)

    Google Scholar 

  3. J.L. Tholence, J. Appl. Phys. 50, 7310 (1979); Solid State Comm. 35, 113 (1980)

    Google Scholar 

  4. E.P. Wohlfarth, Physica 86-88B, 852 (1977); J. Phys. F10, 1,241 (1980); Phys. Lett. 70A, 489 (1979); E.P. Wohlfarth and S. Shtrikman, Phys. Lett. 85A, 467 (1981)

    Google Scholar 

  5. M. Gyrot, Solid State Comm. 39, 1009 (1981)

    Google Scholar 

  6. For a review, see J.A. Mydosh, J. Mag. Magn. Mat. 7, 237 (1978)

    Google Scholar 

  7. G. Eiselt, J. Kötzler, H. Maletta, D. Stauffer and K. Binder, Phys. Rev. B19, 2664 (1979)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. G. Parisi, J. Phys. A13, L115 (1980); Phil. Mag. B41,677 (1980)

    Google Scholar 

  11. H. Sompolinsky, Phys. Rev. Lett. 47, 935 (1981); H. Sompolinsky and A. Zippelius, Phys. Rev. B25, 6860 (1982); J. Hertz, J. Phys. C16, 1219 (1983); 1233 (1983)

    Google Scholar 

  12. A.P. Young, J. Phys. C14, L1085 (1981); A.P. Young and S. Kirkpatrick, Phys. Rev. B25, 440 (1982); A. Houghton, S. Jain and A.P. Young, preprint; N.D. Mackenzie and A.P. Young, Phys. Rev. Lett. 49, 301 (1982), and preprint; A.P. Young and C. de Dominicis, preprint

    Google Scholar 

  13. R.G. Palmer, Adv. Phys. 31, 669 (1982)

    Google Scholar 

  14. J.R.L. De Almeida and D.J. Thouless, J. Phys. A11, 983 (1978)

    Google Scholar 

  15. G. Parisi and G. Thouless, J. Phys. Lett. (Paris) 41, L361 (1980); G. Toulouse, M. Gabay, T.C. Lubensky and J. Vannimenus, J. Phys. Lett. 43, L109 (1982)

    Google Scholar 

  16. M.E. Fisher, Rev. Modern Phys. 46, 597 (1974)

    Google Scholar 

  17. A.B. Harris, T.C. Lubensky, and J.H. Chen, Phys. Rev. Lett. 38, 765 (1976)

    Google Scholar 

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

    Google Scholar 

  19. A.J. Bray and M.A. Moore, J. Phys. F7, L333 (1977); A.J. Bray, M.A. Moore, and P. Reed, J. Phys. C11, 1187 (1978)

    Google Scholar 

  20. A.J. Bray and M.A. Moore, Phys. Rev. Lett. 41, 1068 (1978); J. Phys. C12, 1,441 (1979); see also H. Sompolinsky and A. Zippelius, Phys. Rev. Lett. 50,1294 (1983)

    Google Scholar 

  21. I. Morgenstern and K. Binder, Phys. Rev. Lett. 43, 1615 (1979); Phys. Rev. B22, 288 (1980)

    Google Scholar 

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

    Google Scholar 

  23. J.R. Banavar and M. Cieplak, Phys. Rev. Lett. 82, 832 (1982)

    Google Scholar 

  24. W. Kinzel and K.H. Fischer, J. Phys. C11, 2115 (1978), and references therein

    Google Scholar 

  25. P.W. Anderson and C.W. Pand, Phys. Rev. Lett. 40, 903 (1978)

    Google Scholar 

  26. D. Stauffer and K. Binder, Z. Physik B30, 313 (1978); B34, 97 (1979)

    Google Scholar 

  27. L. Lundgren, P. Svedlindh, and O. Beckmann, Phys. Rev. B26, 3990 (1982)

    Google Scholar 

  28. P. Monod and H. Bouchiat, J. Phys. Lett. (Paris) 43, L45 (1982)

    Google Scholar 

  29. B. Barbara, A.P. Malozemoff, and Y. Imry, Phys. Rev. Lett. 47, 1852 (1981); A.P. Malozemoff, B. Barbara, and Y. Impry, J. Appl. Phys. 53, 2205 (1982)

    Google Scholar 

  30. B. Barbara, A.P. Malozemoff, and Y. Imry, Physica 108B+C, 1289 (1981)

    Google Scholar 

  31. A. Berton, J. Chaussy, J. Odin, B. Rammal, and R. Tournier, J. Phys. Lett.(Pais) 43, L–153 (1982)

    Google Scholar 

  32. R. Omari, J.J. Prejean, and J. Souletie, J. phys. (Paris) in press

    Google Scholar 

  33. J. Ferré, J. Rajchenbach and H. Maletta, J. Appl. Phys. 52, 1967 (1981)

    Google Scholar 

  34. M. Guyot, S. Foner, S.K. Hasanain, R.P. Guertin, and K. Westerhold, Phys. Lett. 79A, 339 (1980)

    Google Scholar 

  35. MB. Salamon, K.V. Rav, and Y. Yeshurun, J. Appl. Phys. 52, 1687 (1981)

    Google Scholar 

  36. R.V. Chamberlin, M. Hardiman, L.A. Turkevich and R. Orbach, Phys. Rev. B25, 6720 (1982)

    Google Scholar 

  37. Y. Yeshurun and H. Sompolinsky, Phys. Rev. B26, 1487 (1982)

    Google Scholar 

  38. N. Bontemps, J. Rajchenbach, and R. Orbach, J. Phys. Lett. (Paris) 44, L47 (1983)

    Google Scholar 

  39. M.B. Salamon, and J.L. Tholence, J. Appl. Phys. 53, 7684 (1982); J. Magn. Mag. Mat., in press

    Google Scholar 

  40. J. Hamida, C. Paulsen, S.J. Williamson, and H. Maletta, preprint

    Google Scholar 

  41. K. Binder and K. Schröder, Phys. Rev. B14, 2142 (1976)

    Google Scholar 

  42. K. Binder, Z. Phys. B26, 339 (1977)

    Google Scholar 

  43. W. Kinzel, Phys. Rev. B19, 4594 (1979)

    Google Scholar 

  44. K. Binder and D. Stauffer, Phys. Lett. 57A, 177 (1976)

    Google Scholar 

  45. Note that finite energy barriers between different ground states need not rule out a phase transition, see P. Hoever, W.F. Wolff, and J. Zittartz, Z. Phys. B41, 43 (1981); B42, 259 (1981); P. Hoever and J. Zittartz, Z. Phys. B44, 129 (1981)

    Google Scholar 

  46. I. Morgenstern, J. Appl. Phys. 53, 7682 (1982); Phys. Rev. B27, 4522 (1983); see also I. Morgenstern, and H. Horner, Phys. Rev. B25, 504 (1982)

    Google Scholar 

  47. W. Kinzel, Z. Phys. B46, 59 (1982)

    Google Scholar 

  48. W. Kinzel, Phys. Rev. B26, 6303 (1982)

    Google Scholar 

  49. K. Binder and I. Morgenstern, Phys. Rev. B27, 5826 (1983)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  52. W. Kinzel and K. Binder, Phys-Rev. Lett. 50, 1509 (1983); and to be published

    Google Scholar 

  53. K. Binder and D. Stauffer, in Monte Carlo Methods in Statistical Physics (K. Binder, ed., Springer, Berlin 1979) p.301; K. Binder, J. Phys. (Paris) 39, C61527 (1978); K. Binder, in Ordering in Strongly Fluctuating Condensed Matter Systems (T. Riste, ed., Plenum Press, New York 1979) p.423; K. Binder and D. Stauffer, in Monte Carlo Methods in Statistical Physics II (K. Binder, ed., Springer, to be published).

    Google Scholar 

  54. H. Hilhorst and B. Derrida, J. Phys. C14, L539 (1981)

    Google Scholar 

  55. J.L. van Hemmen and I. Morgenstern, J. Phys. C15, 4353 (1982)

    Google Scholar 

  56. J.A. Mydosh, J. Phys.Soc. Jpn. 52, Suppl. p.85 (1983)

    Google Scholar 

  57. P.C. Hohenberg and B.I.Halperin, Rev. Mod. Phys. 49, 435 (1977)

    Google Scholar 

  58. I. Morgenstern, Phys. Rev. B25, 6067 (1982)

    Google Scholar 

  59. H. Maletta, J. Phys. (Paris) C6, 115 (1980), and references therein

    Google Scholar 

  60. B. Barbara, and A.P. Malozemoff, Proc. 16th Rare Earth Research Conf., Florida State Univ., April 1983 to be published

    Google Scholar 

  61. It should be noted that the physical significance of the shift of the susceptibility maximum at very small fields can be questioned on a various physical grounds: (i) it may be an artefact due to macroscopic sample inhomogeneities (H. Alloul, private communication) (ii) it may be an effect specific for Heisenberg spins, just as there exists for isotropic Heisenberg antiferromagnets in a field a cuspshaped umbilicus of the critical temperatures.Tc(H),Tc(-H), which merge at the T-axis in a bicritical point (G. Toulouse, private communication). In Ising spin glasses for d<dℓ none of these alternative explanations can apply, however.

    Google Scholar 

  62. These data were obtained in [41] by stepwise decrease of H at constant T, and thus for small H near Tf are slightly affected by observation time effects. The scaling analysis of Sec.IV hence uses more accurate recent simulation data [52] obtained by field-cooling as in Figs.1,2.

    Google Scholar 

  63. J. Chalupa, Solid State Commun. 24, 429 (1977); M. Suzuki, Progr. Theor. Phys. 58, 1151 (1977); K. Binder, Festkörperprobleme 17, 55 (1977)

    Google Scholar 

  64. N. Bontemps and J. Rajchenbach, to be published

    Google Scholar 

  65. K. Binder and W. Kinzel, in Lecture Notes in Physics 149, p.124 (ed. by C. di Castro) Springer Berlin, Heidelberg and New York, 1981.

    Google Scholar 

  66. F. Mezei, in Recent Developments in Condensed Matter Physics ed. J.T. Devreese (Plenum, Press, New York 1981) Vol.l, p.679

    Google Scholar 

  67. D. Hüser, L.E. Wenger, A.J. van Duyneveldt and J.A. Mydosh, Phys. Rev. B, in press

    Google Scholar 

  68. D.E. Mac Laughlin, L.C. Gupta, R.H. Heffner, M. Leon, and M.E. Schillaci, to be published

    Google Scholar 

  69. A.P. Malozemoff and Y. Imry: Phys. Rev. B24, 489 (1981)

    Google Scholar 

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  1. Institut für Festkörperforschung, Kernforschungsanlage Jülich, D-5170, Jülich, W.-Germany

    K. Binder & W. Kinzel

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  1. K. Binder
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J. L. van Hemmen I. Morgenstern

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© 1983 Springer-Verlag

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Binder, K., Kinzel, W. (1983). The spin glass transition: a comparison of Monte Carlo simulations of nearest-neighbor Ising Edwards-Anderson models with experiments. In: van Hemmen, J.L., Morgenstern, I. (eds) Heidelberg Colloquium on Spin Glasses. Lecture Notes in Physics, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12872-7_54

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  • DOI: https://doi.org/10.1007/3-540-12872-7_54

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