We discuss a method to solve models with {\it 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 {\it ensemble inequivalence}. The model Hamiltonian can have both {\em discrete} (Ising, Potts) and {\em 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 $\alpha$-Ising model in one-dimension with $0\leq \alpha<1$.
Large deviation techniques applied to systems with long-range interactions / BARRE' J; BOUCHET F; DAUXOIS T; S. RUFFO. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 119:(2005), pp. 677-713. [10.1007/s10955-005-3768-8]
Large deviation techniques applied to systems with long-range interactions
RUFFO, STEFANO
2005
Abstract
We discuss a method to solve models with {\it 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 {\it ensemble inequivalence}. The model Hamiltonian can have both {\em discrete} (Ising, Potts) and {\em 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 $\alpha$-Ising model in one-dimension with $0\leq \alpha<1$.File | Dimensione | Formato | |
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