Dynamics and thermodynamics of a model with long-range interactions

Pluchino, A.; Latora, V.; Rapisarda, A.
March 2004
Continuum Mechanics & Thermodynamics;Mar2004, Vol. 16 Issue 3, p245
Academic Journal
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.


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