and approximately proportional to the square root of the cluster length, just like a random walk. When folded with the length spectrum, this suggests [@hart98] that the ‘radius spectrum’ should also be described by a power law N(r) = , \[eqn\_rad\_spec\] with $\eta \approx 5$ and $c_r(\beta)$ weakly dependent on $\beta$. Such a spectrum is close to the scale invariant spectrum of 4–dimensional balls of radius $\rho$, $N(\rho) d\rho \sim d\rho/\rho
\times 1/\rho^4$, and so one might try and relate these clusters to the SU(2) instantons in the theory, which classically also possess a scale-invariant spectrum. It is well known, however, that the inclusion of quantum corrections renders the spectrum of the latter far from scale invariant, at least for the small instantons where perturbation theory can be trusted, and so such a connexion does not seem to be possible [@hart98]. On sufficiently large volumes the difference in length between the largest and second largest cluster is very marked, and where this gulf is clear one finds that the long range physics such as the monopole string tension arises solely from the largest cluster. This is the case at $\beta = 2.3$, $L \ge 10$ and at $\beta = 2.4$, 