Core-halo distribution in the Hamiltonian Mean-Field Model
  We study a paradigmatic system with long-range interactions: the Hamiltonian
Mean-Field Model (HMF). It is shown that in the thermodynamic limit this model
does not relax to the usual equilibrium Maxwell-Boltzmann distribution.
Instead, the final stationary state has a peculiar core-halo structure. In the
thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find
that using dynamical properties of Hamiltonian systems, it is possible to
quantitatively predict both the spin distribution and the velocity distribution
functions in the final stationary state, without any adjustable parameters. We
also show that HMF undergoes a non-equilibrium first-order phase transition
between paramagnetic and ferromagnetic states.
