Dynamics of Symmetry Breaking: Phase Coherence in Finite and Random Systems

  • F. de Pasquale
Part of the NATO ASI Series book series (NSSB, volume 116)


Purely relaxational dynamics for an n-component vectorial order parameter has been extensively used to study critical dynamics of Heisenberg magnetic systems (1) and statistical properties of transient laser radiation (2). The dynamical model we are referring to is the TDGL (time-dependent Ginzburg-Landau) model, i.e., non linear Langevin equation describing the evolution of the order parameter associated with the system. Non linearity is usually associated with a coupling between the degrees of freedom typical of the system. Only in the laser case it is possible to select a single degree of freedom (the unimode operation). In such a limit phase coherence phenomenon appears as a consequence of an instability of the system. In the opposite limit of an infinite number of degrees of freedom we have the thermodynamic limit in which the same instability can give rise to a phase transition.


Critical Temperature Correlation Length Linear Relaxation Spherical Limit Random Magnetic Field 
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  1. 1.
    S. K. Ma, Modern theory of critical phenomena, W. Benjamin Inc. (1976)Google Scholar
  2. 2.
    H. Risken and H. D. Vollmer, Z. Phys. 204, 240 (1976)ADSGoogle Scholar
  3. 3.
    F.T. Arecchi, in Order Fluctuations in Equilibrium and Non equilibrium Statistical Mechanics ed. by Nicolis, G. Dewel and J.W. Turner, Willey New York, 1981 p. 107.Google Scholar
  4. 4.
    Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)ADSCrossRefGoogle Scholar
  5. 5.
    F. de Pasquale, Z. Racz and P. Tartaglia, Phys. Rev. B sept. 1983Google Scholar
  6. 6.
    K. Binder, W. Kinzel: in “Disordered Systems and Localization” Lecture Notes in Physics 149 (1981) ed. by C. Castellani, C. Di Castro and L. Peliti.Google Scholar
  7. 7.
    S. Fishman, A. Ahrony, J. Phys. C 12, L729 (1979)ADSCrossRefGoogle Scholar
  8. 8.
    F. T. Arecchi, V. Degiorgio and B. Querzola, Phys. Rev. Lett. 19, 1168 (1967)ADSCrossRefGoogle Scholar
  9. 9.
    F. de Pasquale, P. Tartaglia and P. Tombesi, Phys. Rev. A25, 466 (1982)ADSGoogle Scholar
  10. 10.
    J.S. Langer, Ann. Phys. 65, 53 (1971)ADSCrossRefGoogle Scholar
  11. 11.
    D. Sherrington, the same issue of ref. 6Google Scholar
  12. 12.
    I. Halperin, P. C. Hohenberg and S.K. Ma, Phys. Rev. Lett. 29, 1548 (1972)ADSCrossRefGoogle Scholar
  13. 13.
    Z. Racz, T. Tel, Phys. Lett. 60A, 3 (1977)ADSGoogle Scholar
  14. 14.
    J. D. Gunton, M. San Miguel and P. Sahni, “The Dynamics of firs order phase transitions” to appear in “Phase transitions and critical phenomena” ed. by C. Domb and J. Levowitz (Academic Press)Google Scholar
  15. 15.
    R. J. Birgenau et al., Phys. Rev. 28, 1438 (1983)ADSCrossRefGoogle Scholar
  16. 16.
    G. Parisi, N. Surlas, Phys. Rev. Lett. 43, 744 (1979)ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • F. de Pasquale
    • 1
  1. 1.Dipartimento di FisicaUniversità di Roma, “La Sapienza”RomaItaly

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