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

概要

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The exact short-time expansion coefficients of the two-time spin-pair correlation function σ(R_<if>,t)=≪s_i^2(t)s_f^2(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 t^<10> for the Heisenberg magnet on the linear chain, and those up to the term of t^8 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 I^^⌒_s(k), the Laplace-time Fourier-space transform of σ(R_<if>,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.
理論物理学刊行会の論文
1980-10-25