one would expect from a random walk. Folded with a length spectrum $N(l)
\sim 1/l^3$, this gives $\eta = 5$. On the $L=32$ lattice we still find that the random walk [*ansatz*]{} provides an acceptable fit but we also find that $r(l) = s + t.l^{0.65}$ works equally well over similar ranges. The latter, when folded with $\gamma = 3$, gives $\eta
= 4.2$. It is clear that the direct calculation of $N(r)$ is much more accurate than the indirect approach.

Treating the power as a free parameter in the fit, $r(l) = s + t.l^u$, we find $u = 0.57$ (3) on $L=32$ at $\beta = 2.5115$, consistent with $u = 0.58$ (4) on $L=20$ at $\beta=2.5$. Thus both $u=0.5$ and $u=0.65$ lie within about two standard deviations from the fitted value. Note that what the fitted powers $\gamma$ and $u$ parameterise are the means of the distributions of lengths and radii respectively. That combining these does not give the directly calculated value of $\eta$ is not unexpected, and reflects the importance of fluctuations around the mean in the distributions.

If the secondary monopole clusters can be associated with localised excitations of the full SU(2) vacuum (‘4–balls’), it would 