Upper Marginal Dimensionality. Concept and Experiment

  • Jens Als-Nielsen
  • Ib Laursen
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 50)


A broad class of second-order phase transitions have the same qualitative features. In order to describe these it is convenient to use the nomenclature of one particular type of system, and we shall chose the language of magnetic systems. It is emphasized that simply by changing a few words the following description may be adapted to describe any second-order phase transition; for example, in the case of the gas-liquid transition around the critical point insert “density” for “magnetization”, “pressure” for “magnetic field”, and “compressibility” for “susceptibility”.


Critical Behavior Correlation Range Field Behavior Tetragonal Axis Ising Ferromagnet 
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.


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  1. 1.
    The following 3 sections follow the exposition given in J. Als-Nielsen and R.J. Birgeneau, Am. J. Phys. 45, 554 (1977).ADSCrossRefGoogle Scholar
  2. 2.
    H.E. Stanley, Introduction to Phase Transition and Critical Phenomena (Oxford U.P., London, 1971).Google Scholar
  3. 3.
    W. Marshall and R.D. Lowde, Rep. Prog. Phys. 31, 705 (1968).ADSCrossRefGoogle Scholar
  4. 4.
    J.S. Smart, Effective Field Theories of Magnetism (Saunders, Philadelphia, 1966).Google Scholar
  5. 5.
    Below the critical temperature the critical indices for susceptibility and correlation range are conventionally denoted y’ and v’.Google Scholar
  6. 6.
    V.L. Ginzburg, Sov. Phys. Solid State 2, 1824 (1960).MathSciNetGoogle Scholar
  7. 7.
    R. Bausch, Z. Phys. 254, 81 (1972).ADSCrossRefGoogle Scholar
  8. 8.
    J. Als-Nielsen and O.W. Dietrich, Phys. Rev. 153, 706 (1967);ADSCrossRefGoogle Scholar
  9. 8a.
    J. Als-Nielsen and O.W. Dietrich, Phys. Rev. 153, 711 (1967);ADSCrossRefGoogle Scholar
  10. 8b.
    J. Als-Nielsen and O.W. Dietrich, Phys. Rev. 153, 717 (1967);ADSCrossRefGoogle Scholar
  11. 8c.
    J. Als-Nielsen, Phys. Rev. 185, 664 (1969);ADSCrossRefGoogle Scholar
  12. 8d.
    J.C Norwell and J. Als-Nielsen, Phys. Rev. B2, 277 (1970);ADSGoogle Scholar
  13. 8e.
    O. Rathmann and J. Als-Nielsen, Phys. Rev. 9, 3924 (1974).Google Scholar
  14. 9.
    M.E. Fisher and R.J. Burford, Phys. Rev. 156, 583 (1967).ADSCrossRefGoogle Scholar
  15. 10.
    E.J. Samuelsen, Phys. Rev. Lett. 31, 936 (1973),ADSCrossRefGoogle Scholar
  16. 10a.
    H. Ikeda, I. Hatta, A. Ikushima, and K. Hirakawa, J. Phys. Soc. Jpn. 39, 827 (1975).ADSCrossRefGoogle Scholar
  17. 11.
    J. Als-Nielsen, Phys. Rev. Lett. 37, 1161 (1976).ADSCrossRefGoogle Scholar
  18. 12.
    A.I. Larkin and D.E. Khemel’nitzkii, Zh. Eksp. Teor. Fiz. 56, 2087 (1969) [Sov. Phys. JETP 29, 1123 (1969)].Google Scholar
  19. 13.
    A. Aharony, Phys. Rev. B8, 3363 (1973),ADSGoogle Scholar
  20. 13a.
    A. Aharony, Phys. Rev. 9, 3946(E) (1974).ADSGoogle Scholar
  21. 14.
    L.M. Holmes, T. Johansson, and H.J. Guggenheim, Solid State Commun. 12, 993 (1973).ADSCrossRefGoogle Scholar
  22. 15.
    L.M. Holmes, H.J. Guggenheim, and J. Als-Nielsen, in Proceedings of the Ninth International Conference on Magnetism, Moscow, U.S.S.R., 1973 (Nauka, Moscow, U.S.S.R., 1974, Vol. VI, p. 256.Google Scholar
  23. 16.
    J. Als-Nielsen, L.M. Holmes, and H.J. Guggenheim, Phys. Rev. Lett. 32, 610 (1970);ADSCrossRefGoogle Scholar
  24. 16a.
    L.M. Holmes, J. Als-Nielsen, and H.J. Guggenheim, Phys. Rev. B12, 180 (1975).ADSGoogle Scholar
  25. 17.
    The specific heat data of Ashman and Handler, Phys. Rev. Lett. 23, 642 (1969) were analyzed byADSCrossRefGoogle Scholar
  26. 17b.
    Baker and Essam, J. Chem. Phys. 55, 86l (1971) and the data in Fig. 3 is taken from the latter reference.CrossRefGoogle Scholar
  27. 18.
    G. Ahlers, A. Kornblitt, and H.J. Guggenheim, Phys. Rev. Lett. 34, 1227 (1975).ADSCrossRefGoogle Scholar
  28. 19.
    R. Frowein, J. Kötzler and W. Assmus, Phys. Rev. Lett. 42, 739 (1979).ADSCrossRefGoogle Scholar
  29. 20.
    A. Aharony and B.I. Halperin, Phys. Rev. Lett. 35, 1308 (1975).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Jens Als-Nielsen
    • 1
  • Ib Laursen
    • 2
  1. 1.Risø National LaboratoryRoskildeDenmark
  2. 2.Lab. ElectrophysicsTechnical UniversityLyngbyDenmark

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