spins, it is convenient to use $N_0 \equiv V/\langle |C| \rangle \propto
L^{1+\eta}$ single update steps as unit of time. This is then directly comparable with other schemes that attempt moves for all spins in one update step. All our autocorrelation times refer to this unit of time (Metropolis-equivalent unit) which can always be achieved by a rescaling of the time variable.

For the susceptibility we typically find $\tau \approx 1.5 - 2.0$. The values of $\tau$ for each simulation are given in Table 1. Already our rough estimate of $\tau$ shows that for large system sizes the single-cluster update clearly outperforms the Metropolis algorithm, for which the exponential autocorrelation time $\tau_0$ has recently been determined [@r19] to be $\tau_0 = a L^z$, with amplitude[^1] $a \approx
3.76$ and dynamical critical exponent $z = 1.94(6)$. For our largest lattice size $L$=48 this implies a reduction of the autocorrelation time by about three orders of magnitude. A more detailed study of the autocorrelations is in preparation.

To extract the critical exponents we have performed two sets of simulations; one in the critical region where the correlation length of the infinite system is much larger than the linear system size, $\xi_\infty \gg 