Sixth Frequency Moment of the Frequency-Wave-Vector-Dependent Correlation Function for Isotropic Heisenberg Paramagnets at Elevated Temperatures
- 1 May 1970
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 1 (9), 3671-3684
- https://doi.org/10.1103/physrevb.1.3671
Abstract
We calculate the sixth frequency moment of the frequency-wave-vector-dependent spectral function for the isotropic Heisenberg paramagnet at elevated temperatures with arbitrary spin and arbitrary range of exchange interaction. These exact results are compared with the approximate sixth moment predicted by the two-parameter Gaussian representation used in the preceding paper for the generalized diffusivity. The general agreement of the approximate and the exact results for is satisfactory. For the exactly soluble spin-½ nearest-neighbor one-dimensional model, we compare the predictions of the two-parameter Gaussian approximation for and against the exact results for these moments (which are derived by using the corresponding exact spectral function given by Katsura et al. The agreement is again found to be satisfactory. This reinforces our confidence in the qualitative validity of the simple Gaussian approximation for the generalized diffusivity.
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