Free energies in the presence of electric and magnetic fields

TL;DR

This paper reviews various free energies for materials under static electric and magnetic fields, clarifying their Hamiltonians, thermodynamic implications, and relevance to Landau theory of phase transitions.

Contribution

It provides a comprehensive comparison of free energies and Hamiltonians for electric and magnetic fields, clarifying their roles in thermodynamics and statistical mechanics.

Findings

Different free energies correspond to specific Hamiltonians.

The appropriate Hamiltonian depends on the calculation context.

The Landau function is key to understanding phase transitions.

Abstract

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions.