Two-Time Spin-Pair Correlation Function of the Heisenberg Magnet at Infinite Temperature

The two-time spin-pair autocorrelation function σ(→0,t) and the Fourier-space transform I(→k,t) of the two-time spin-pair correlation function σ(→Rif,t), are expressed in terms of the "friction function" occurring in the generalized Langevin equation for the spin operator sᵢ^~ and its Fourier-space transform S_→kᶻ, respectively. The friction function is determined in the form of a product of a Gaussian distribution function and a power series as a function of time t for the isotropic Heisenberg magnet and the XY magnet of spin {} at infinite temperature. By truncating the power series to the exactly known term, satisfactory results are obtained for I(→k,t) of the isotropic Heisenberg magnet of the linear chain and sc lattice. Satisfactory results for σ(→Rif,t) are achieved by taking an inverse Fourier-space transform of the thus determined I(→k,t).