Finite size scaling in CP(N-1) models

Finite size effects in Euclidean ${\mathrm{C}\mathrm{P}}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1\mathrm{/}N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and correlation length are compared and found to agree for small volumes. For large volumes a discrepancy is found and explained as an effect of the physical bound state extension. The leading order finite size effects on the Abelian string tension are computed and compared with simulations finding agreement. Finite size dependence of topological quantities is also discussed.