  We investigate the critical relaxational dynamics of the S=1/2 Heisenberg
ferromagnet on a simple cubic lattice within the Handscomb prescription on
which it is a diagrammatic series expansion of the partition function that is
computed by means of a Monte Carlo procedure. Using a phenomenological
renormalization group analysis of graph quantities related to the spin
susceptibility and order parameter, we obtain precise estimates for the
critical exponents relations $\gamma / \nu = 1.98\pm 0.01 $ and $\beta /\nu =
0.512 \pm 0.002$ and for the Curie temperature $k_BT_c/J = 1.6778 \pm 0.0002$.
The critical correlation time of both energy and susceptibility is also
computed. We found that the number of Monte Carlo steps needed to generate
uncorrelated diagram configurations scales with the system's volume. We
estimate the efficiency of the Handscomb method comparing its ability in
dealing with the critical slowing down with that of other quantum and classical
Monte Carlo prescriptions.
