High Temperature Susceptibility of Permanent Dipole Lattices

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Abstract
Van Vleck's exact classical treatment of dipolar materials is modified and extended. (For convenience, his expansion of the susceptibility χ in powers of T−1 is replaced by an expansion of the effective molecular polarizability αs.) The present procedure exhibits the dependence of the coefficients of T−p on lattice sums over certain typical interactions within ``clusters'' of dipoles. This feature, together with an extension to the fourth‐order term, sheds light on the analytic character as well as numerical accuracy of the spherical approximation. The exact treatment also provides a standard of comparison for all other approximation methods. The fourth‐order coefficient is evaluated for a simple cubic arrangement of the dipoles, and for the Onsager liquid model. The spherical result, at least in the high temperature range, includes the most important types of interactions within clusters; it reproduces the exact series through the third‐order term, and differs from the exact simple‐cubic fourth‐order term by only 5 percent. In addition, when evaluated for the Onsager liquid model, the spherical solution is apparently an improvement over Onsager's solution.
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