Long-time dynamics of the infinite-temperature Heisenberg magnet

Infinite-temperature long-time dynamics of Heisenberg model H^=-1/2${\mathit{tsum}}_{\mathit{i},}$${\mathit{jJ}}_{\mathit{i}\mathit{j}}$S${\mathrm{^}}_{\mathit{i}}$⋅S${\mathrm{^}}_{\mathit{j}}$ is investigated. It is shown that the quantum-spin pair correlator is equal to the correlator of a classically evaluated vector field averaged over the initial conditions with respect to the Gaussian measure. In the continuous-limit case, the scaling estimations allow one to find the one-point correlator that turns out to be C(r=0;t)∝const×${\mathit{t}}^{\mathrm{-}6/7}$. All results are obtained by straightforward procedures without any assumptions of the phenomenological character.