errors by standard jackknife-blocking [@r27].

Binder parameter $U_L(\beta)$
-----------------------------

We have used the histogram reweighting technique to find the $\beta$-dependence of the Binder parameter [@bi82], $$U_L(\beta) = 1 - \frac{1}{3}\frac{\langle m^4\rangle }{\langle m^2\rangle ^2}.
\label{eq:15}$$ To obtain a single curve $U_L(\beta)$ for each lattice size $L$ from the three simulations at temperatures compiled in Table 1 we used our optimized combination of eq. (\[eq:30\]). In (\[eq:15\]) we adapt the usual normalization convention, although the factor 3 is only really motivated for the Ising ($O(1)$) model. For general $O(n)$ models it is easy to show that in the high-temperature limit Gaussian fluctuations around $\vec{m}=0$ lead to $U_L
\rightarrow  2(n-1)/3n$. For $n=1$ this gives a zero reference point, but for the Heisenberg model with $n=3$ we get the quite arbitrary looking limit $U_L \rightarrow 4/9$. In three dimensions, we are for low temperatures always in the magnetized phase and hence have for all $n$ trivially $U_L \rightarrow 2/3$.

It is well known [@bi82] that the $U_L(\beta)$ curves for different $L$ cross around $(\beta_c,U^{*})$ with slopes $\propto L^{1/\nu}$, apart from confluent corrections explaining small systematic deviations. This allows an almost unbiased estimate of $\beta_c$, the critical exponent $\nu$, and $U^{*}$. Field theoretical expansions 