Shape-Dependent Thermodynamic Quantities in Magnetic Systems with Dipole Interaction

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Abstract
If dipolar forces in magnetic materials are comparable to the exchange interactions, the thermodynamic properties in an external applied field are, in general, dependent on the shape of the sample. Recently, Levy has shown that shape-independent thermodynamic properties can be defined from a free energy at given internal field, rather than at given external field. This result is generalized to include anisotropic exchange interaction and arbitrarily oriented ellipsoidal samples. Functional-derivative techniques allow a more condensed notation for the problem. The results given here hold in any order of perturbation theory.