Spin-correlation functions in the paramagnetic phase of a Heisenberg ferromagnet

A method previously presented for the approximate calculation of the time-dependent spin correlations at high temperatures is generalized to apply throughout the paramagnetic phase. It yields static spin correlations in agreement with the predictions of the spherical model. An ad hoc modification of the approximations is suggested which leads to better agreement of the static correlations with the Pade-approximant determination of the susceptibility in the critical regime. The scheme has been used to calculate the inelastic neutron scattering line shapes and widths throughout the paramagnetic phase for the particular case of a simple cubic ferromagnet with nearest neighbour interactions. In the critical regime it reproduces the dynamic scaling laws and allows the calculation of some of the associated universal functions. The minimum line width is found to occur at a temperature above the critical temperature and the shapes and widths of the lines are found to vary rapidly near the critical point.