Metastability and anomalous behavior in the HMF Model: connections to nonextensive thermodynamics and glassy dynamics

TL;DR

This paper reviews recent findings on the Hamiltonian Mean Field model, highlighting its anomalous dynamics, connections to nonextensive thermodynamics, and glassy behavior, emphasizing weak-ergodicity breaking.

Contribution

It provides a comprehensive analysis linking the HMF model's anomalies to nonextensive thermodynamics and glassy dynamics, offering new insights into its complex behavior.

Findings

Identification of dynamical anomalies in the HMF model

Interpretation of anomalies via weak-ergodicity breaking

Connections established between HMF dynamics and nonextensive thermodynamics

Abstract

We review some of the most recent results on the dynamics of the Hamiltonian Mean Field (HMF) model, a systems of N planar spins with ferromagnetic infinite-range interactions. We show, in particular, how some of the dynamical anomalies of the model can be interpreted and characterized in terms of the weak-ergodicity breaking proposed in frameworks of glassy systems. We also discuss the connections with the nonextensive thermodynamics proposed by Tsallis.