Statistical Mechanics of systems with long range interactions

TL;DR

This paper reviews the statistical mechanics of systems with long-range interactions, highlighting their unique properties such as ensemble inequivalence, negative specific heat, and slow relaxation, which differ from short-range systems.

Contribution

It provides a comprehensive overview of the theoretical understanding of long-range interacting systems and discusses models exhibiting these unconventional features.

Findings

Ensemble inequivalence in long-range systems

Negative microcanonical specific heat observed

Slow relaxation processes with diverging time scales

Abstract

Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d dimensions. As a result, these systems are non-additive and they display unusual thermodynamic and dynamical properties which are not present in systems with short range interactions. In particular, the various statistical mechanical ensembles are not equivalent and the microcanonical specific heat may be negative. Long range interactions may also result in breaking of ergodicity, making the maximal entropy state inaccessible from some regions of phase space. In addition, in many cases long range interactions result in slow relaxation processes, with time scales which diverge in the thermodynamic limit. Various models which have been found to exhibit these features are discussed.