Correlation Functions for a Heisenberg Ferromagnet

It is shown that the ac longitudinal susceptibility of a Heisenberg ferromagnet is proportional to the Fourier transform of a dynamical $\mathrm{zz}$ correlation function of the spins, $z$ being the direction of the spontaneous magnetization. The susceptibility can also be calculated by the Tyablikov decoupling approximation. Hence, the dynamical $\mathrm{zz}$ correlation function is obtained by taking the inverse Fourier transform of the latter result. This expression for the correlation function is an interpolation formula which agrees with the noninteracting spin-wave theory at very low temperatures and with the statistical theory at very high temperatures. The applications of these correlation functions to specific heat, susceptibility, and electrical conductivity are also discussed.