Landau’s Theory of Phase Transitions

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)


Landau’s theory concerns the kind of invariants consistent with the symmetry of the crystal that may appear in the expression for the free energy. In this sense, it should be viewed as one of the successful applications of the group theory in classical physics. Unlike ordinary classical applications, however, the representation theory for space groups plays an essential role here, because a change of crystal symmetry is the main issue. It is most interesting to note that possible types of phase transitions are determined definitely solely from symmetry considerations.


Irreducible Representation Brillouin Zone Identity Representation Symmetry Operation Lower Eigenvalue 
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  1. 14.1
    L. D. Landau, E. M. Lifshitz: Statistical Physics, Part 1, 3rd ed. (Pergamon, Oxford 1980) pp. 446–471Google Scholar
  2. 14.2
    A detailed treatment without using group theory is given by T. Nagamiya: “Helical Spin Ordering” in Solid State Physics, Vol. 20, ed. by F. Seitz, D. Turnbull, H. Ehrenreich (Academic, New York 1967) pp. 305–411Google Scholar
  3. 14.3
    J. M. Kosterlitz, D. J. Thouless: J. Phys. C 6, 1181 (1973)ADSCrossRefGoogle Scholar
  4. 14.4
    W. F. Brinkman, R. J. Elliott: Proc. R. Soc. London 294A, 343 (1966)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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