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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Feng, Jonathan

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Volume 10, Issue 3

Issues

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

Pierre Buyl
  • Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050, Brussels, Belgium
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/ Duccio Fanelli
  • Dipartimento di Energetica “S. Stecco” and CSDC, University of Florence, CNISM and INFN, Via S. Marta 3, 50139, Florence, Italy
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/ Stefano Ruffo
  • Dipartimento di Energetica “S. Stecco” and CSDC, University of Florence, CNISM and INFN, Via S. Marta 3, 50139, Florence, Italy
  • Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, 69364, Lyon cédex 07, France
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Published Online: 2012-06-17 | DOI: https://doi.org/10.2478/s11534-012-0010-6

Abstract

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.

Keywords: long-range interactions; Vlasov equation; Lynden-Bell theory

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About the article

Published Online: 2012-06-17

Published in Print: 2012-06-01


Citation Information: Open Physics, Volume 10, Issue 3, Pages 652–659, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-012-0010-6.

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