done this time in the high-temperature phase. There we use variance reduced “cluster estimators” [@r10a] for the spatial correlation length, $\xi$, and the susceptibility, $\chi$. By going to very large systems with up to $100^3$ spins we have made sure that these data have only negligible finite-size corrections well below the statistical errors of about $0.2\%$. Least-square fits of the critical divergencies of $\xi$ and $\chi$ to the well-known power-laws yield independent estimates for the critical coupling and the critical exponents $\nu$ and $\gamma$. Obviously this is another useful check on residual systematic errors. Finally, in Sec. 5, we briefly discuss and summarize our main results.

The model and simulation techniques
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Let us start with a brief description of the model and some remarks on the simulation techniques we have used. The partition function of the Heisenberg model is given by $$Z = \prod_{{\mbox{\boldmath $x$}}} \left[ \int
\frac{d\phi({\mbox{\boldmath $x$}})d\cos\theta({\mbox{\boldmath $x$}})}{4\pi} \right] e^{-\beta E},
\label{eq:1}$$ where $\beta \equiv J/k_BT$ is the (reduced) inverse temperature and the energy is $$E = \sum_{{\mbox{\boldmath $x$}},i} \left[
1-\vec{s}({\mbox{\boldmath $x$}})\vec{s}({\mbox{\boldmath $x$}}+{\mbox{\boldmath $i$}}) \right].
\label{eq:2}$$ Here $\vec{s} = (\sin \theta \cos \phi, \sin \theta \sin \phi,
\cos \theta)$ are three-dimensional unit spins at the sites ${\mbox{\boldmath 