Thermodynamics of the HMF model with a magnetic field

TL;DR

This paper explores the complex thermodynamics of the HMF model with an external magnetic field, revealing rich phenomena like negative specific heats, ensemble inequivalence, phase transitions, and ergodicity breaking, especially when metastable states are considered.

Contribution

It introduces the analysis of metastable states in the HMF model with a magnetic field, uncovering new thermodynamic behaviors and phase transition phenomena.

Findings

Identification of negative specific heats in microcanonical ensemble.

Observation of ensemble inequivalence and zeroth order phase transitions.

Detection of ergodicity breaking due to magnetization gaps.

Abstract

We study the thermodynamics of the Hamiltonian Mean Field (HMF) model with an external potential playing the role of a "magnetic field". If we consider only fully stable states, this system does not present any phase transition. However, if we take into account metastable states (for a restricted class of perturbations), we find a very rich phenomenology. In particular, the system displays a region of negative specific heats in the microcanonical ensemble in which the temperature decreases as the energy increases. This leads to ensembles inequivalence and to zeroth order phase transitions similar to the "gravothermal catastrophe" and to the "isothermal collapse" of self-gravitating systems. In the present case, they correspond to the reorganization of the system from an "anti-aligned" phase (magnetization pointing in the direction opposite to the magnetic field) to an "aligned" phase (magnetization pointing in the same direction as the magnetic field). We also find that the magnetic susceptibility can be negative in the microcanonical ensemble so that the magnetization decreases as the magnetic field increases. The magnetic curves can take various shapes depending on the values of energy or temperature. We describe hysteretic cycles involving positive or negative susceptibilities. We also show that this model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking.