Remarks about the thermostatistical description of the HMF model Part I: Equilibrium Thermodynamics

TL;DR

This paper provides a detailed microcanonical thermodynamic analysis of the HMF model, a long-range interacting system, including entropy, observables, and stability, laying groundwork for understanding its equilibrium properties.

Contribution

It offers the first comprehensive microcanonical thermodynamic description of the HMF model, focusing on entropy, stability, and thermodynamic limit analysis.

Findings

Calculated microcanonical entropy and thermodynamic observables

Analyzed distribution and correlation functions

Assessed thermodynamic stability and limits

Abstract

In this series of papers we shall carry out a reconsideration of the thermodynamical behavior of the called HMF model, a paradigmatic ferromagnetic toy model exhibiting many features of the real long-range interacting systems. This first work is devoted to perform the microcanonical description of this model system: the calculation of microcanonical entropy and some fundamental thermodynamic observables, the distribution and correlation functions, as well as the analysis of the thermodynamical stability and the relevant thermodynamic limit.