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Analytical results on the magnetization of the Hamiltonian Mean-Field model |
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| Authors: | R Bachelard C Chandre D Fanelli YY Yamaguchi |
| Institution: | a Synchrotron Soleil, L'Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette cedex, France b Centre de Physique Théorique, CNRS - Aix-Marseille Universités, Campus de Luminy, case 907, F-13288 Marseille cedex 09, France c Dipartimento di Energetica “Sergio Stecco”, Università di Firenze, via s. Marta 3, 50139 Firenze, Italy d Centro interdipartimentale per lo Studio delle Dinamiche Complesse (CSDC), Italy e INFN, Italy f Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto, Japan |
| Abstract: | 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. |
| Keywords: | 05 70 Ln 05 45 -a 05 70 Fh 45 50 Pk |
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