Core-halo distribution in the Hamiltonian Mean-Field Model

Details Core-halo distribution in the Hamiltonian Mean-Field Model Core-halo distribution in the Hamiltonian Mean-Field Model

2010-11-30

arxiv.org/abs/1012.0035v2

Phys.Rev.Lett.106:200603,2011

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevLett.106.200603

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.

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