Large deviation techniques applied to systems with long-range interactions

TL;DR

This paper presents an adaptation of large deviation techniques to solve models with long-range interactions, enabling analysis of ensemble inequivalence and non-equilibrium effects across various models.

Contribution

It extends existing large deviation methods to a broader class of models with both discrete and continuous variables, including slowly decreasing interactions.

Findings

Solution of alpha-Ising model in 1D for 0 ≤ α < 1

Demonstration of ensemble inequivalence in long-range models

Access to non-equilibrium dynamics analysis

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 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 $0\leq\alpha<1$.