Dynamical Properties of the Diluted Heisenberg and XY Magnets at Infinite Temperature. I: Spin Diffusion Constant

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Abstract
The exact short-time expansion coefficients of the two-time spin-pair correlation function σ(Rif,t)=≪siz(t)sfz(0)≫c at infinite temperature are used in order to estimate the spin diffusion constants of the diluted Heisenberg and XY magnets of spin 1/2. The used coefficients are those up to the term of t10 for the Heisenberg magnet on the linear chain, and those up to the term of t8 for the Heisenberg and XY magnets on the square, sc and bcc lattices. Our calculations are based on the “linear extrapolation approximation”, in which unknown coefficients in Mori's continued fraction representation for ~Is(k), the Laplace-time Fourier-space transform of σ(Rif,t), are linearly extrapolated from the last two of the known coefficients. The obtained values of the diffusion constant and their concentration dependences show a reasonable trend of convergence for successive approximations in a range of concentration not close to the percolation limit. Discussions are also given on the diffusion constants obtained by the “two-parameter Gaussian approximation in time” applied to the memory function.

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