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Phys. Rev. Lett. 77, 3645–3648 (1996)

[Issue 17 – October 1996 ]

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Near-Surface Long-Range Order at the Ordinary Transition

Uwe Ritschel and Peter Czerner
Fachbereich Physik, Universität GH Essen, 45117 Essen, FR Germany
Received 28 February 1996

We study the spatial dependence of the order parameter m(z) near surface that reduces the tendency to order. Using scaling arguments and perturbative methods ( epsilon expansion), we find that for T >= Tbc a small surface magnetic field h1 gives rise to a macroscopic length scale and an anomalous short-distance increase of m(z), governed by the power law m~z kappa (with kappa =1- eta ordperp~=0.21 for the d = 3 Ising model). This result is related to experiments where exponents of the ordinary transition were observed in Fe3Al, while superstructure reflections revealed the existence of long-range order near the surface.

©1996 The American Physical Society

URL: http://publish.aps.org/abstract/PRL/v77/p3645
PACS: 75.40.Cx, 68.35.Rh, 75.30.Pd, 78.70.Ck


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References

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  1. For reviews on surface critical phenomena, see K. Binder, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London,1983), Vol. 8, and Ref. [2].
  2. H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London,1986), Vol. 10.
  3. H. W. Diehl and S. Dietrich, Z. Phys. B 42, 65 (1981); 43, 281(E) (1981).
  4. S. Dietrich and H. Wagner, Phys. Rev. Lett. 51, 1469 (1983); Z. Phys. B 56, 207 (1984).
  5. X. Mailänder, H. Dosch, J. Peisl, and R. L. Johnson, Phys. Rev. Lett. 64, 2527 (1990).
  6. For a review of the experimental work, see H. Dosch, in Critical Phenomena at Surfaces and Interfaces, edited by G. Höhler and E. A. Niekisch, Springer tracts in Modern Physics (Springer, Berlin,1992).
  7. F. Schmid, Z. Phys. B 91, 77 (1993).
  8. From the power-law decay m~z- beta / nu at the extraordinary transition, it appears that the magnetization diverges when going towards the surface. One has to bear in mind, however, that the power law is only valid for distances much larger than microscopic scales. Upon approaching the surface, the magnetization would depart from the power law and assume a finite value in the surface.
  9. C. Ruge, S. Dunkelmann, and F. Wagner, Phys. Rev. Lett. 69, 2465 (1992).
  10. A. J. Bray and M. A. Moore, J. Phys. A 10, 1927 (1977).
  11. H. W. Diehl and T. W. Burkhardt, Phys. Rev. B 50, 3894 (1994).
  12. E. Brézin and S. Leibler, Phys. Rev. B 27, 594 (1983).
  13. A. Ciach and H. W. Diehl (unpublished).
  14. H. W. Diehl, G. Gompper, and W. Speth, Phys. Rev. B 31, 5841 (1985).
  15. The correct scaling field at the ordinary transition is actually h1/cy0, where the exponent y = 1 in MF theory but [not equal] 1 in general. It is discussed in detail in Ref. [2] that, in the framework of the loop expansion, one does not capture the deviation from the MF value in this exponent, while, e.g., the z dependence of expectation values is reproduced correctly. For details, we refer to Refs. [2] and [14].
  16. G. Gompper, Z. Phys. B 56, 217 (1984).
  17. This is in accord with, and actually motivated by, the field-theoretical short-distance expansion [see K. Symanzik, Nucl. Phys. B190(FS3), 1 (1981); H. W. Diehl and S. Dietrich, Z. Phys. B 42, 65 (1981)], where field operators near a boundary are expressed in terms of boundary operators multiplied by c-number functions.
  18. The relation m1~h1 seems to be inconsistent with the definition of the surface exponent delta 11 via m1~h1/ delta 111 and the result delta ord11~=0.6 for the Ising model [2]. One has to bear in mind, however, that delta ord11 governs the leading singular behavior of m1 which is weaker here than the linear dependence on h1 [10].
  19. H. K. Janssen, B. Schaub, and B. Schmittmann, Z. Phys. B 73, 539 (1989).
  20. H. W. Diehl and U. Ritschel, J. Stat. Phys. 73, 1 (1993); U. Ritschel and H. W. Diehl, Phys. Rev. E 51, 5392 (1995); Nucl. Phys. B464, 512 (1996).
  21. T. C. Lubensky and M. H. Rubin, Phys. Rev. B 12, 3885 (1975).
  22. M. Smock and H. W. Diehl, Phys. Rev. B 47, 5841 (1993).
  23. L. V. Mikheev and M. S. Fisher, Phys. Rev. B 49, 378 (1994).
  24. N. S. Desai, S. Peach, and C. Franck, Phys. Rev. E 52, 4129 (1995).


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