Spin Pair Correlation in the Heisenberg Ferromagnet

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Abstract
The spin pair correlations in the Heisenberg ferromagnet are studied by employing the diagrammatical technique of Stinchcombe et al. The first order terms in the z-1-expansion in Brout's sense for the longitudinal spin pair correlation yield the Ornstein-Zernike result in the Weiss approximation, whereas the next order terms contain the effects of the spin-wave-like collective modes which give rise to the 1/q term in the Fourier transform of the longitudinal spin pair correlation for the isotropic Heisenberg ferromagnet below the Curie point for small q, the wave vector. This term dominates the Ornstein-Zernike part for small enough q. This supports the results obtained by the Green's function method given by Mori and the author. The recent criticisms by Oguchi and Ono on our Green's function work are repudiated.

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