Non-Gaussian equilibrium in a long-range Hamiltonian system

We study the dynamics of a system of N classical spins with infinite-range interaction. We show that, when the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions and dynamical power-law correlation in phase-space.