tells us that that the length of the largest cluster is proportional to the volume at fixed lattice spacing: $l_{\max}
\propto L^4$. The fact that the various horizontal lines almost coincide tells us that the current density in the largest cluster is consistent with scaling. That is to say, it has a finite non-zero value in the continuum limit. Thus the monopole whose world line traces out this largest cluster, percolates throughout the space–time volume and its world line is sufficiently smooth on short distance scales that its length does not show any sign of diverging as we take the continuum limit. We note that the $L=32$ lattice deviates by $\sim
10\%$ from the other values. This is consistent with what we might have expected from the different gauge fixing procedure used in that case.

Turning now to the secondary clusters, we display in Figure \[fig\_len\_spec\] the length spectrum that we obtain at $\beta=2.5115$. It is clearly well described by a power law as in eqn. \[eqn\_len\_spec\] and we fit the exponent to be $\gamma =
3.01$ (8). This is in accord with the universal value of 3 that was postulated in [@hart98] on the basis of calculations on coarser 