2004/06/30 by Julien Barré, Julien Barre', Freddy Bouchet +2 · 2 citations
Physics and Astronomy · #Canonical ensemble #Extension (predicate logic) #Hamiltonian (control theory) #Large deviations theory #Microcanonical ensemble #Quantum many-body systems #Range (aeronautics) #Simple (philosophy) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-005-3768-8
published as Journal of Statistical Physics 119, 677-713 (2005)
arxiv created 2005/02/14 · openalex publication_date 2005/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 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-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with 0≤α<1.