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Central European Journal of Physics

, Volume 10, Issue 3, pp 652–659 | Cite as

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

  • Pierre de BuylEmail author
  • Duccio Fanelli
  • Stefano Ruffo
Research Article

Abstract

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.

Keywords

long-range interactions Vlasov equation Lynden-Bell theory 

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References

  1. [1]
    A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009)MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    T. Dauxois, S. Ruffo, L. Cugliandolo (Eds.), Long-Range Interacting Systems, Lecture Notes of the Les Houches Summer School: Volume 90, August 2008, Oxford University Press (2009)Google Scholar
  3. [3]
    Y.Y. Yamaguchi, J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, Physica A 337, 36 (2004)ADSCrossRefGoogle Scholar
  4. [4]
    A. Antoniazzi, F. Califano, D. Fanelli, S. Ruffo, Phys. Rev. Lett. 98, 150602 (2007)ADSCrossRefGoogle Scholar
  5. [5]
    J. Barré, T. Dauxois, G. De Ninno, D. Fanelli, S. Ruffo, Phys. Rev. E 69, 045501(R) (2004)ADSCrossRefGoogle Scholar
  6. [6]
    D. Lynden-Bell, R. Wood, Mon. Not. R. Astron. Soc. 138, 495 (1968)ADSGoogle Scholar
  7. [7]
    Y. Y. Yamaguchi, Phys. Rev. E 78, 041114 (2008)ADSCrossRefGoogle Scholar
  8. [8]
    M. Joyce, T. Worrakitpoonpon, J. Stat. Mech. P10012 (2010)Google Scholar
  9. [9]
    M. Antoni, S. Ruffo, Phys. Rev. E 52 (1995)Google Scholar
  10. [10]
    P. H. Chavanis, Eur. Phys. J. B 53, 487 (2006)ADSCrossRefGoogle Scholar
  11. [11]
    A. Antoniazzi, D. Fanelli, S. Ruffo, Y.Y. Yamaguchi, Phys. Rev. Lett. 99, 040601 (2007)ADSCrossRefGoogle Scholar
  12. [12]
    G. De Ninno, D. Fanelli, Europhys. Lett. 97, 20002 (2012)CrossRefGoogle Scholar
  13. [13]
    P. H. Chavanis, Eur. Phys. J. B 80, 275 (2011)ADSCrossRefGoogle Scholar
  14. [14]
    F. Staniscia, P. H. Chavanis, G. De Ninno, Phys. Rev. E. 83, 051111 (2011)ADSCrossRefGoogle Scholar
  15. [15]
    S. Ogawa, Y. Y. Yamaguchi, Phys. Rev. E. 84, 061140 (2011)ADSCrossRefGoogle Scholar
  16. [16]
    R. Bachelard, C. Chandre, D. Fanelli, X. Leoncini, S. Ruffo, Phys. Rev. Lett. 101, 260603 (2008)ADSCrossRefGoogle Scholar
  17. [17]
    J. Barré, Y. Y. Yamaguchi, Phys. Rev. E. 79, 036208 (2009)ADSCrossRefGoogle Scholar
  18. [18]
    Y. Y. Yamaguchi, Phys. Rev. E. 84, 016211 (2011)ADSCrossRefGoogle Scholar
  19. [19]
    P. de Buyl, Commun. Nonlinear Sci. Numer. Simulat. 15, 2133 (2010)ADSzbMATHCrossRefGoogle Scholar
  20. [20]
    R. Pakter, Y. Levin, Phys. Rev. Lett. 106, 200603 (2011)ADSCrossRefGoogle Scholar
  21. [21]
    P. de Buyl, D. Mukamel, S. Ruffo, Phil. Trans. R. Soc. A 369, 439 (2011)ADSzbMATHCrossRefGoogle Scholar
  22. [22]
    P. de Buyl, D. Mukamel, S. Ruffo, Phys. Rev. E 84, 061151 (2011)ADSCrossRefGoogle Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2012

Authors and Affiliations

  • Pierre de Buyl
    • 1
    Email author
  • Duccio Fanelli
    • 2
  • Stefano Ruffo
    • 2
    • 3
  1. 1.Center for Nonlinear Phenomena and Complex SystemsUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Dipartimento di Energetica “S. Stecco” and CSDCUniversity of Florence, CNISM and INFNFlorenceItaly
  3. 3.Laboratoire de Physique de l’École Normale Supérieure de LyonUniversité de Lyon, CNRSLyon cédex 07France

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