Theory of Critical-Point Scattering and Correlations. II. Heisenberg Models

The spin-spin correlation functions and the critical-scattering intensity for Heisenberg models of general spin, S=12 to, on the sc, bcc, and fcc lattices are studied on the basis of high-temperature series expansions along the lines developed in Paper I M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967). Subject to increased uncertainties for low spin, it is concluded that the exponents =1. 375-₀. ₀₁^+0. 02, 2=1. 405-₀. ₀₁^+0. 02, and =0. 0430. 014 describe all lattices and all spin. Explicit formulas are presented for the susceptibility/zero-angle scattering ₀ (T), for the inverse correlation length ₁ (T), for the effective interaction range r₁ (T), and using the Fisher-Burford approximant, for the total scattering ^ (k, T). The shape parameter ₂ attains the "universal" value ₂0. 11 for large spin but shows signs of spin dependence (and lattice dependence) for low spin. At fixed k the scattering is predicted to display a maximum above T₂ determined by {₁ (T₌₀ₗ) }k0. 10 (for S2) to 0. 15. A detailed study is made of the structure dependence of the critical-point correlations 〈{S₀^zS{r}^z〉}₂ for various models. This leads to the revised, universal estimate ₂0. 15 for all three cubic lattice, spin- Ising models. The results are compared d briefly with various experiments which support 0. 05.