Advertisement

Higher-Order Critical Points in Magnetic Systems

  • R. M. Hornreich
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 48)

Abstract

Some of the most outstanding successes of the modern theory of critical phenomena have occurred as a consequence of theoretical and experimental studies of so-called higher-order critical or multicritical points. In general, a phase transition occurs when a given thermodynamic parameter (usually temperature) reaches a special or critical value. However, in many cases it is possible to vary a magnetic system’s behavior by varying other accessible thermodynamic parameters (e.g., pressure, stress, or applied electric and magnetic fields). Within the phase diagram generated by this set of parameters, the usual critical point develops into a critical line or surface. While many properties of the system near a critical point are asymptotically independent of its location on the critical surface, there can exist special points on the surface characterized by different critical behavior. The characteristics of these higher-order critical points will be the subject of these lectures. We shall discuss in particular tricritical, bicritical, and Lifshitz points. In view of the program of this school, we shall develop the theoretical models in terms of magnetic systems and materials.

Keywords

Critical Exponent Critical Line Tricritical Point NATO Advance Study Institute Multicritical Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.M. Hornreich, K.A. Penson, and S. Shtrikman, J. Phys. Chem. Solids 33, 433 (1972).CrossRefADSGoogle Scholar
  2. 2.
    Basic references to the theory of tricritical behavior include: R.B. Griffiths, Phys. Rev. Lett. 24, 715 (1970); D.R. Nelson and M.E. Fisher, Phys. Rev. B 11, 1030 (1975); M.E. Fisher, AIP Conf. Proc. 24, 273 (1975); M.J. Stephen, E. Abrahams, and J.P. Straley, Phys. Rev. B 12, 256 (1975); D.R. Nelson, AIP Conf. Proc. 29, 450 (1976); I.D. Lawrie, J. Phys. C 13, 2739 (1980).CrossRefADSGoogle Scholar
  3. 3.
    W.P. Wolf, Proc. NATO Advanced Study Institute on Multicritical Phenomena, Geilo, Norway, April 1983.Google Scholar
  4. 4.
    Basic references to the theory of bicritical points include: M.E. Fisher and D.R. Nelson, Phys. Rev. Lett. 32, 1350 (1974); A. Aharoni and A.D. Bruce, Phys. Rev. Lett. 33, 427 (1974); A.D. Bruce and A. Aharoni, Phys. Rev. B 11 478 (1975); M.E. Fisher, AIP Conf. Proc. 24, 273 (1975); J.M. Kosterlitz, D.R. Nelson, and M.E. Fisher, Phys. Rev. B 13, 412 (1976); D. Mukamel, Phys. Rev. B 14 1303 (1976).CrossRefADSGoogle Scholar
  5. 5.
    S. Galam and A. Aharoni, J. Phys. C 13, 1065 (1980); Ibid, C 14, 3606 (1981).ADSGoogle Scholar
  6. 6.
    Y. Shapira, Proc. NATO Advanced Study Institute on Multicritical Phenomena, Geilo, Norway, April 1983.Google Scholar
  7. 7.
    The Lifshitz point was introduced in R.M. Hornreich, M. Luban, and S. Shtrikman, Phys. Rev. Lett. 35, 1678 (1975); for a review and extensive references to the literature, see R.M. Hornreich, J. Mag. Magn. Mater. 15–18, 387 (1980).CrossRefADSGoogle Scholar
  8. 8.
    S.K. Ma, Modem Theory of Critical Phenomena (W.A. Benjamin, New York 1976).Google Scholar
  9. 9.
    R.M. Hornreich and A.D. Bruce, J. Phys. A 11, 595 (1978); D. Mukamel, J. Phys. A10, L249 (1977).ADSGoogle Scholar
  10. 10.
    See, e.g., R.M. Hornreich, R. Liebmann, H.G. Schuster, and W. Selke, Z. Phys. B 35, 91 (1979); W. Selke and M.E. Fisher, Z. Phys. B 40, 71 (1980); J. Villain and P. Bak, J. de Physique 42, 657 (1981); M.N. Barber and P.M. Duxburg, J. Stat. Phys. 29, 427 (1982).ADSGoogle Scholar
  11. 11.
    S. Osthund, Phys. Rev. B 24, 398 (1981), S. Howes, L.P. Kadanoff, and M. den Jigs, Nucl. Phys. B 215, 169 (1983); W. Selke and J.M. Yeomans, Z. Phys. B 46, 311 (1982).ADSGoogle Scholar
  12. 12.
    B. Schaub and E. Domany, Phys. Rev. B-August 1983 issue.Google Scholar
  13. 13.
    L.P. Kadanoff, Ann. Phys. 100, 359 (1976).CrossRefADSGoogle Scholar
  14. 14.
    R.M. Hornreich, k. Liebmann, H.G. Schuster, and W. Selke, Z. Physik B 35, 91 (1979).ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • R. M. Hornreich
    • 1
  1. 1.Department of ElectronicsWeizmann Institute of ScienceRehovotIsrael

Personalised recommendations