  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.
