Ensemble thermodynamic potentials of magnetic systems

The analogy between magnetic systems and fluids is explored and the corresponding thermodynamic potentials of the microcanonical, canonical, and conjugate intensive variable (field) ensembles are analyzed. It is shown that the discrepancy criteria of the magnetic free energy obtained when working within the canonical ensemble, as can be seen in a variety of text books on statistical mechanics, are in fact because one is actually working in the field ensemble instead. The disagreement, however, is more a question about the name given to the thermodynamic potential than on the underlying principles of the theory. Examples of the spin-1/2 paramagnet and the one-dimensional Ising model are discussed in detail.