Phenomenological description of dynamics in diluted isotropic Heisenberg paramagnet at high temperatures

We consider a diluted isotropic Heisenberg paramagnet at infinite temperature. Frequency moments of the wave-vector-frequency-dependent spin correlation function are calculated up to the fourth moment for arbitrary concentration $m$ of the magnetic atoms. Employing phenomenological procedures based upon the use of a two-parameter Gaussian form for the generalized diffusivity, we estimate the concentration dependence of the spin-diffusion coefficient. This result is expected to be qualitatively reasonable as long as the concentration of nonmagnetic atoms is small, i.e., for $1-m\ll 1$. However, for large vacancy concentration, i.e., $m\ll 1$, our mean-field-theory-like result must break down because we expect the magnetization diffusion to cease below some critical concentration $m_c$, because then all the exchange connected clusters will be of finite size. This is an interesting point and we note that it should be investigated by computer-experiment techniques (which are well established for the undiluted case when $S=\infty$). Finally, we present results for the frequency- (or time-) and wave-vector- (or space-) dependent correlation functions for the simple cubic lattice for the two limiting cases, $S=\frac{1}{2}$ and $S=\infty$.