High-temperature series for the B-site spinel and diamond lattices and the question of universality

The high-temperature series for the two-spin correlation functions on both the B-site spinel and diamond lattices have been calculated through tenth order for the Hamiltonian, H=−JΣ〈 ij 〉 Σα=1n(n≤ D) SiαSjα. Here Siα is the αth component of the D-dimensional classical spin and we define n as the spin space symmetry parameter. By <ij> we limit the first summation to nearest-neighbor pairs of sites i and j on the lattice. The spin space symmetry parameter n is ≤D. We consider all six models resulting from D=1–3. Our analysis of the high-temperature series indicates that while the exponent estimates for the more loosely packed diamond lattice (q=4) indicate agreement with the universality hypothesis, the B-site spinel lattice (q=6) series are not yet displaying their critical behavior. Some conjectures concerning this peculiarity of the series for the two lattices are made.