On statistical mechanics of instantons in the CPNc−1 model

Abstract We introduce an explicit form of the multi-instanton weight including also instanton–anti-instanton interactions for arbitrary Nc in the two-dimensional CPNc−1 model. To that end, we use the parametrization of multi-instantons in terms of instanton `constituents' which we call `zindons' for short. We study the statistical mechanics of zindons analytically (by means of the Debye–Huckel approximation) and numerically (running a Metropolis algorithm). Though the zindon parametrization allows for a complete `melting' of instantons we find that, through a combination of dynamical and purely geometric factors, a dominant portion of topological charge is residing in well-separated instantons and anti-instantons.