  Monte Carlo studies of $CP^{N-1}$ sigma models have shown that the structure
of topological charge in these models undergoes a sharp transition at
$N=N_c\approx 4$. For $N<N_c$ topological charge is dominated by small
instantons, while for $N>N_c$ it is dominated by extended, thin,
1-dimensionally coherent membranes of topological charge, which can be
interpreted as domain walls between discrete quasi-stable vacua. These vacua
differ by a unit of background electric flux. The transition can be identified
as the delocalization of topological charge, or "instanton melting," a
phenomenon first suggested by Witten to resolve the conflict between instantons
and large $N$ behavior. Implications for $QCD$ are discussed.
