Skip to main content
SpringerLink
Log in

Critical behavior of a degenerate ferromagnet in a uniaxial random field: Exact results in a space of arbitrary dimension

  • Solids
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The critical behavior of the transverse (with respect to the field) magnetization component in classical degenerate magnets with only nearest-neighbors interaction in a uniaxial random magnetic field at zero temperature is found exactly. For a Gaussian distribution of the random field the asymptotic transverse magnetization in strong fields does not depend on the dimension of the space and is of the form m ⊥ ∝ 1nh 0/h 20 , where h 0 is the width of the distribution. For a bimodal distribution, where only the field direction is random and the amplitude is fixed, the transverse magnetization behaves as m ⊥∝exp(−const/(H c −H)D/2), where H is the amplitude of the random field, D is the dimension of the space, and H c is the critical field.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. P. Belanger and A. P. Young, J. Magn. Magn. Mater. 100, 272 (1991).

    Article  ADS  Google Scholar 

  2. V. S. Dotsenko, Usp. Fiz. Nauk 165, 481 (1995).

    Google Scholar 

  3. T. Nattermann, E-prints archive cond-mat/9705295 (1997).

  4. S. Fishman and A. Aharony, J. Phys. C 12, L729 (1979).

    Article  ADS  Google Scholar 

  5. D. P. Belanger, A. R. King, V. Jaccarino, and J. L. Cardy, Phys. Rev. B 28, 2522 (1983).

    Article  ADS  Google Scholar 

  6. Ch. Binek, S. Kuttler, and W. Kleemann, Phys. Rev. Lett. 75, 2412 (1995).

    Article  ADS  Google Scholar 

  7. J. Villain, J. Physique Lett. 43, 808 (1982).

    Google Scholar 

  8. C. Bostoen and K. H. Michel, Z. Phys. B 71, 369 (1988).

    Article  Google Scholar 

  9. T. Nattermann, Ferroelectrics 104, 171 (1990).

    Google Scholar 

  10. P. G. de Gennes, J. Phys. Chem. 88, 6469 (1984).

    Google Scholar 

  11. J. V. Porto and J. M. Parpia, Phys. Rev. Lett. 74, 4667 (1995).

    Article  ADS  Google Scholar 

  12. J. Hook, Bull. Am. Phys. Soc. 42, 799 (1997).

    Google Scholar 

  13. K. Matsumoto, J. V. Porto, L. Pollak et al., Phys. Rev. Lett. 79, 253 (1997).

    ADS  Google Scholar 

  14. N. A. Clark, T. Bellini, R. M. Malzbender et al., Phys. Rev. Lett. 71, 3505 (1993).

    Article  ADS  Google Scholar 

  15. H. Haga and C. W. Carland, Liq. Cryst. 22, 275 (1997).

    Google Scholar 

  16. G. Blatter, M. V. Feigelman, V. B. Geshkenbein, and A. I. Larkin, Rev. Mod. Phys. 66, 1125 (1994).

    Article  ADS  Google Scholar 

  17. T. Giamarchi and P. Le Doussal, E-prints archive cond-mat/9705096 (1997).

  18. A. Aharony, Y. Imry, and S.-K. Ma, Phys. Rev. Lett. 37, 1364 (1976).

    ADS  Google Scholar 

  19. A. P. Young, J. Phys. C 10, L257 (1977).

    Article  ADS  Google Scholar 

  20. G. Parisi and N. Sourlas, Phys. Rev. Lett. 43, 744 (1979).

    ADS  Google Scholar 

  21. J. Imbrie, Phys. Rev. Lett. 53, 1747 (1984).

    Article  ADS  Google Scholar 

  22. J. Imbrie, Commun. Math. Phys. 98, 145 (1985).

    Article  MathSciNet  Google Scholar 

  23. J. Bricmont and A. Kupiainen, Phys. Rev. Lett. 59, 817 (1987).

    Article  MathSciNet  Google Scholar 

  24. M. Gofman, J. Adler, A. Aharony et al., Phys. Rev. B 53, 6362 (1996).

    Article  ADS  Google Scholar 

  25. G. Parisi, in Proceedings of Les Houches 1982,Session XXXIX, edited by J. B. Zuber and R. Stora (North Holland, Amsterdam, 1984).

    Google Scholar 

  26. J. Villain, J. de Phys. 46, 1843 (1985).

    Google Scholar 

  27. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).

    Google Scholar 

  28. K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1993).

    Google Scholar 

  29. G. Parisi, J. Phys. A 13, 1887 (1980).

    ADS  MathSciNet  Google Scholar 

  30. V. S. Dotsenko, Usp. Fiz. Nauk 163(6), 1 (1993).

    Google Scholar 

  31. M. Mezard and A. P. Young, Europhys. Lett. 18, 653 (1992).

    ADS  Google Scholar 

  32. S. E. Korshunov, Phys. Rev. B 48, 3969 (1993).

    ADS  Google Scholar 

  33. M. Mezard and R. Monasson, Phys. Rev. B 50, 7199 (1994).

    ADS  Google Scholar 

  34. T. Giamarchi and P. Le Doussal, Phys. Rev. B 52, 1242 (1995).

    Article  ADS  Google Scholar 

  35. D. E. Feldman, Phys. Rev. B 56, 3167 (1997).

    Article  ADS  Google Scholar 

  36. E. Farhi and S. Gutman, Phys. Rev. B 48, 7114 (1993).

    Article  Google Scholar 

  37. M. Schwartz, Phys. Lett. A 76, 408 (1980).

    ADS  MathSciNet  Google Scholar 

  38. R. M. Hornreich and H. G. Schuster, Phys. Rev. B 26, 3929 (1982).

    Article  ADS  Google Scholar 

  39. T. Vojta, J. Phys. A 26, 2883 (1993).

    Article  ADS  Google Scholar 

  40. T. Vojta and M. Schreiber, Phys. Rev. B 50, 1272 (1994).

    Article  ADS  Google Scholar 

  41. D. E. Feldman, J. Phys. A 31, L177 (1998).

    Article  ADS  MATH  Google Scholar 

  42. A. Aharony, Phys. Rev. B 18, 3328 (1978).

    ADS  Google Scholar 

  43. V. S. Dotsenko and M. V. Feigelman, J. Phys. C 14, L823 (1981).

    Article  ADS  Google Scholar 

  44. B. J. Minchau and R. A. Pelcovits, Phys. Rev. B 32, 3081 (1985).

    Article  ADS  Google Scholar 

  45. D. C. Mattis, Phys. Lett. A 56, 421 (1976).

    Article  ADS  Google Scholar 

  46. R. Bidraux, J. P. Carton, and G. Sarma, Phys. Lett. A 58, 467 (1976).

    ADS  Google Scholar 

  47. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, New York) [Russian original, Nauka, Moscow, 1982].

  48. R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. L. D. Landau Institute of Theoretical Physics, 142432, Chernogolovka, Moscow Region, Russia

    D. É. Fel’dman

Authors
  1. D. É. Fel’dman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Zh. Éksp. Teor. Fiz. 115, 2143–2159 (June 1999)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fel’dman, D.É. Critical behavior of a degenerate ferromagnet in a uniaxial random field: Exact results in a space of arbitrary dimension. J. Exp. Theor. Phys. 88, 1170–1178 (1999). https://doi.org/10.1134/1.558907

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.558907

Keywords

Search

Navigation