Phase transitions of quasistationary states in the Hamiltonian Mean Field model

• Authors: Pierre Buyl , Duccio Fanelli , Stefano Ruffo
• Languages of publication: EN

Abstracts

EN

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

EN

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

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 652-659

Dates

published

1 - 6 - 2012

online

17 - 6 - 2012

Contributors

author

Pierre Buyl

• Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050, Brussels, Belgium

author

Duccio Fanelli

• Dipartimento di Energetica “S. Stecco” and CSDC, University of Florence, CNISM and INFN, Via S. Marta 3, 50139, Florence, Italy

author

Stefano Ruffo

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Identifiers

DOI

10.2478/s11534-012-0010-6