2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202472We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box and use them to interpret the strong finite size effects observed in lattice simulations at medium values of $N$. The asymptotic scaling behaviour of alternative lattice actions is discussed along with some aspects of multigrid algorithm efficiency.6 pages of text plus 2 pages of figures, Liverpool Preprint LTH283High Energy Physics - Latticetext