(\[eq:14\]). For each $L$ and $\beta$ we obtained in this way three estimates of $\frac {dU_L} {d\beta}(\beta)$ that we combined optimally according to the errors of $\frac {dU_L} {d\beta}$.

In Fig. 4 we plot $\frac {dU_L} {d\beta} (\beta_c)$, taken at our estimate of $\beta_c=0.6930$, versus $L$ on a log-log scale. From the inverse slope we read off $$\nu = 0.704 \pm 0.006, \label{eq:18}$$ with a quality factor $Q$=0.61, relying on the linear least-square fit routine FIT of ref. [@r24]. For comparison, the field theoretical estimates are $\nu = 0.705(3)$ (resummed perturbation series [@zi80]), $\nu = 0.710(7)$ (resummed $\epsilon$-expansion [@zi85]). We noted that the value of $\nu$ derived in this way was strongly dependent on the temperature at which it was extracted. It turned out that the systematic errors one gets by choosing a slightly different value for $\beta_c$ are larger than the statistical errors. The strong $\beta$-dependence of $\frac {dU_L} {d\beta}$ has its origin in the large system sizes we used that make the thermodynamic quantities vary very rapidly with $\beta$. For comparison, for $\beta=0.6929$ ($\beta=0.6931$) we obtained $\nu=0.696(6)$ with $Q$=0.76 ($\nu=0.712(6)$ with $Q$=0.49); see also Fig. 8 below.

Magnetization and susceptibility
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To extract the ratio of critical exponents 