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The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back

  • Thierry Dauxois
  • Vito Latora
  • Andrea Rapisarda
  • Stefano Ruffo
  • Alessandro Torcini
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 602)

Abstract

The thermodynamics and the dynamics of particle systems with infiniterange coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a paradigmatic example of this class of systems. The present study addresses both attractive and repulsive interactions, with a particular emphasis on the description of clustering phenomena from a thermodynamical as well as from a dynamical point of view. The observed clustering transition can be first or second order, in the usual thermodynamical sense. In the former case, ensemble inequivalence naturally arises close to the transition, i.e. canonical and microcanonical ensembles give different results. In particular, in the microcanonical ensemble negative specific heat regimes and temperature jumps are observed. Moreover, having access to dynamics one can study non-equilibrium processes. Among them, the most striking is the emergence of coherent structures in the repulsive model, whose formation and dynamics can be studied either by using the tools of statistical mechanics or as a manifestation of the solutions of an associated Vlasov equation. The chaotic character of the HMF model has been also analyzed in terms of its Lyapunov spectrum.

Keywords

Lyapunov Exponent Field Model Physical Review Order Phase Transition Canonical Ensemble 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thierry Dauxois
    • 1
  • Vito Latora
    • 2
    • 3
  • Andrea Rapisarda
    • 2
    • 3
  • Stefano Ruffo
    • 1
    • 4
  • Alessandro Torcini
    • 4
    • 5
  1. 1.Laboratoire de Physique, UMR CNRS 5672ENS LyonLyonFrance
  2. 2.Dipartimento di FisicaUniversitá di CataniaItaly
  3. 3.Sezione di CataniaIstituto Nazionale di Fisica NucleareCataniaItaly
  4. 4.Dipartimento di Energetica “S. Stecco”Università di FirenzeFirenzeItaly
  5. 5.UMR-CNRS 6171Université d’Aix-Marseille IIIMarseille Cedex 20France

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