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

Free energies in the presence of electric and magnetic fields