+ \sum_{k=1}^{\infty} A(k)$, which describes the enhancement of the statistical error, $\epsilon = \sqrt{\sigma^2/N} \sqrt{2\tau}$, for the mean value over a sample of $N$ correlated measurements of variance $\sigma^2$. The infinite sum was always self-consistently cut off at $k_{\rm max} \approx 6 \tau$ [@madras; @book1; @book2].

Recall that for the single-cluster update some care is necessary in defining the unit of time, since in each update step only a relatively small fraction of the spins is moved, depending on temperature and lattice size. More precisely, our results show that near $\beta_c$ and for all lattice sizes, the average cluster size, $\langle |C| \rangle$, is proportional to the susceptibility, $$\langle |C| \rangle \approx 0.75 \bar{\chi}
\label{eq:9}$$ (with roughly the same constant as in two dimensions [@r10a]), where $\bar{\chi} = \chi/\beta = V \langle \vec{m}^2 \rangle$, $\vec{m} = \frac {1}{V} \sum_{{\mbox{\boldmath $x$}}}
\vec{s}({\mbox{\boldmath $x$}})$. At $\beta_c$, the susceptibility behaves like $\chi \propto
L^{\gamma/\nu}=L^{2-\eta}$ (with very small $\eta \approx
0.04$), so that with increasing lattice size the fraction of moved spins in each update step decreases like $\langle |C| \rangle/V \propto L^{-(1+\eta)}$, i.e., roughly $\propto 1/L$. Since the CPU time needed for a single-cluster update is approximately proportional to the number of moved 