The Topological Susceptibility of the Lattice CP(n-1) Model on the Torus and the Sphere

The topological vacuum structure of the two-dimensional $C{P}^{n-1}$ model for $n=3,5,7$ is studied on the lattice. In particular we investigate the small-volume limit on the torus as well as on the sphere and compare with continuum results. For $n\ge 5$ , where lattice artifacts should be suppressed, the topological susceptibility shows unexpectedly strong deviations from asymptotic scaling. On the other hand there is an indication for a convergence to values obtained analytically within the limit $~n \rightarrow \infty~$ .