Large Deviation Techniques Applied to Systems with Long-Range Interactions |
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Authors: | Julien Barré Freddy Bouchet Thierry Dauxois Stefano Ruffo |
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Affiliation: | (1) Laboratoire de Physique, ENS Lyon, UMR-CNRS 5672, 46 Allée d’Italie, 69364 cédex 07, Lyon, France;(2) Theoretical Division, Los Alamos National Laboratory, USA;(3) Dipartimento di Energetica, “S. Stecco” and CSDC, Università di Firenze, and INFN, via S. Marta,3, 50139 Firenze, Italy |
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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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Keywords: | long-range interactions large deviation techniques mean-field limit |
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