Analytical results on the magnetization of the Hamiltonian Mean Field model

Details Analytical results on the magnetization of the Hamiltonian Mean Field model Analytical results on the magnetization of the Hamiltonian Mean Field model

2009-03-21

arxiv.org/abs/0903.3641v1

Physics Letters A 373, 46 (2009) 4239

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1016/j.physleta.2009.09.037

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high and low energy limits are investigated and the analytical predictions are compared with direct $N$-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.

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