Do Instantons of the CP(N-1) Model Melt?

In the two-dimensional CP^N-l model one can parametrize exact many-instanton solutions via N 'constituents' (called 'zindons'). This parameterization allows, in principle, a complete 'melting' of individual instantons. The model is therefore well suited to study whether dynamics prefers a dilute or a strongly overlapping ensemble of instantons. We study the statistical mechanics of instantons both analytically and numerically. We find that at N = 2 the instanton system collapses into zero-size instantons. At N = 3,4 we find that well-isolated instantons are dynamically preferred though 15-25% of instantons have a considerable overlap with others.