An exactly soluble model of a system containing arbitrary isotropic bilinear and biquadratic exchange interactions

Stanley's exact results for a Bethe Lattice of classical spins of arbitrary dimensionality are generalized to include an arbitrary biquadratic interaction term. Simple expressions are obtained for both the nearest neighbor dipolar and quadrupolar correlation functions. It is shown that the system never displays long range order at any finite temperature. A modest amount of biquadratic excahnge can even prevent the system from ordering at T = 0°K. However, except for the linear chain, two distinct temperatures are found for the divergence of the dipolar and quadrupolar susceptibilities.