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Large Deviation Techniques Applied to Systems with Long-Range Interactions

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Abstract

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.

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Authors and Affiliations

  1. Laboratoire de Physique, ENS Lyon, UMR-CNRS 5672, 46 Allée d’Italie, 69364, cédex 07, Lyon, France

    Julien Barré, Freddy Bouchet, Thierry Dauxois & Stefano Ruffo

  2. Theoretical Division, Los Alamos National Laboratory, USA

    Julien Barré

  3. Dipartimento di Energetica, “S. Stecco” and CSDC, Università di Firenze, and INFN, via S. Marta,3, 50139, Firenze, Italy

    Stefano Ruffo

Authors
  1. Julien Barré
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  2. Freddy Bouchet
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  3. Thierry Dauxois
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  4. Stefano Ruffo
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Correspondence to Thierry Dauxois.

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Barré, J., Bouchet, F., Dauxois, T. et al. Large Deviation Techniques Applied to Systems with Long-Range Interactions. J Stat Phys 119, 677–713 (2005). https://doi.org/10.1007/s10955-005-3768-8

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  • DOI: https://doi.org/10.1007/s10955-005-3768-8

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