Analytical results on the magnetization of the Hamiltonian Mean Field model

Romain Bachelard (1) , Cristel Chandre (2, 3) , Antonia Ciani (4) , Duccio Fanelli (4) , Yoshiyuki Y. Yamaguchi (5)

1 SSOLEIL - Synchrotron SOLEIL
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332
4 dip. energetica
5 Department of Applied Mathematics and Physics [Kyoto]

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.

Mots clés: Vlasov equation; Hamiltonian systems; Out-of-equilibrium phase transition

Domaines: Dynamique Chaotique [nlin.CD]

Romain Bachelard, Cristel Chandre, Antonia Ciani, Duccio Fanelli, Yoshiyuki Y. Yamaguchi. Analytical results on the magnetization of the Hamiltonian Mean Field model. Physics Letters A, 2009, 373 (46), pp.4239. ⟨10.1016/j.physleta.2009.09.037⟩. ⟨hal-00369725⟩