Topological susceptibility of the 2D or O(3) nonlinear model: Is it divergent or not?

The topological susceptibility of 2D CPN-1 models is expected, based on perturbative computations, to develop a divergence in the limit N -> 2, where these models reduce to the well-known nonlinear O(3) sigma model. The divergence is due to the dominance of instantons of arbitrarily small size and its detection by numerical lattice simulations is notoriously difficult, because it is logarithmic in the lattice spacing. We approach the problem from a different perspective, studying the behavior of the model when the volume is fixed in dimensionless lattice units, where perturbative predictions are turned into more easily checkable behaviors. After testing this strategy for N = 3 and 4, we apply it to N = 2, adopting at the same time a multicanonic algorithm to overcome the problem of rare topological fluctuations on asymptotically small lattices. Our final results fully confirm, by means of purely nonperturbative methods, the divergence of the topological susceptibility of the 2D CP1 model.