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

The two‐time spin‐pair correlation function σ(R,t) is expressed as a product of a Gaussian distribution function and a power series with respect to time. The width of the Gaussian distribution function is determined by the second derivative with respect to time of the autocorrelation function σ(0,t). The coefficients of the power series are determined up to terms of order t⁸ for the square and s.c. isotropic Heisenberg and XY magnets of spin ½ at infinite temperature, and up to terms of t¹⁰ for the linear magnets. The expressions obtained by truncating the power series to the exactly known terms give a very good fit at short times to the exact expression for the linear XY model, and to the results of the computer simulation due to Windsor for the s.c. Heisenberg ferromagnet. The Fourier‐time transforms of the expressions thus obtained are shown to be the Gram‐Charlier expansions. Thus we conclude that the Gram‐Charlier expansion of the Fourier‐time transform of $\mathrm{\sigma (R,t),\sigma ̃(R,\omega )}$ , and that of its Fourier‐space transform I(k,t),S(k,ω), is especially useful in the cases when the short‐time behavior of σ(R,t) or I(k,t) is considered important; generally speaking, this is the case at large k or at ω which is not very small. When the width of the Gaussian distribution function is determined by the second derivative of I(k,t), a convergent result is not obtained for small values of k. For larger k, the convergence is as good as for the case when the width is determined by the autocorrelation function.