on the standard local heatbath [@r15] or Metropolis [@r16; @r17] algorithm. In a recent series of papers Peczak [*et al.*]{} [@r18; @r19] used the latter algorithm combined with histogram reweighting techniques [@oldpaper; @r20; @r21; @r22] to estimate the critical coupling and the critical exponents of the 3D Heisenberg model from a FSS analysis of simulations on simple cubic lattices [@r18] and investigated also its (exponential) autocorrelation time $\tau_0$ [@r19]. Their result, $\tau_0 \propto L^z$, with dynamical critical exponent $z = 1.94(6)$, shows that $\tau_0$ is rapidly increasing with the linear lattice size $L$ and explains why they could not go to systems larger than $24^3$. Since, as expected, the autocorrelation time for the single-cluster algorithm turns out to be almost independent of $L$ we could study much larger lattices of size up to $48^3$ in reasonable computer time. Our results described in Sec. 3 provide evidence that the asymptotic FSS region is indeed reached quite early or, in other words, that the amplitudes of correction terms are very small. The present study thus significantly reduces the danger of systematic errors in the MC estimates of critical exponents from FSS analyses.

In Sec. 4 we report another set of high-precision simulations, 