Continuum Mechanics and Thermodynamics

, Volume 16, Issue 3, pp 245–255 | Cite as

Dynamics and thermodynamics of a model with long-range interactions

  • A. Pluchino
  • V. Latora
  • A. RapisardaEmail author
Original article


The dynamics and thermodynamics of particles/spins interacting via long-range forces display several unusual features compared with systems with short-range interactions. The Hamiltonian mean field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions represents a paradigmatic example of this class of systems. The equilibrium properties of the model can be derived analytically in the canonical ensemble: in particular, the model shows a second-order phase transition from a ferromagnetic to a paramagnetic phase. Strong anomalies are observed in the process of relaxation towards equilibrium for a particular class of out-of-equilibrium initial conditions. In fact, the numerical simulations show the presence of quasi-stationary states (QSS’s), i.e. metastable states that become stable if the thermodynamic limit is taken before the infinite time limit. The QSS’s differ strongly from Boltzmann-Gibbs equilibrium states: they exhibit negative specific heats, vanishing Lyapunov exponents and weak mixing, non-Gaussian velocity distributions and anomalous diffusion, slowly decaying correlations, and aging. Such a scenario provides strong hints for the possible application of Tsallis generalized thermostatistics. The QSS’s have recently been interpreted as a spin-glass phase of the model. This link indicates another promising line of research, which does not preclude to the previous one.


phase transitions Hamiltonian dynamics long-range interaction out-of-equilibrium statistical mechanics 


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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Dipartimento di Fisica e AstronomiaUniversitá di Catania, and INFN Sezione di CataniaCataniaItaly

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