Corrections to Finite - Size Scaling in the

We compute the corrections to nite-size scaling for the N-vector model on the square lattice in the large-N limit. We nd that corrections behave as log L=L 2. For tree-level improved hamiltonians corrections behave as 1=L 2. In general l-loop improvement is expected to reduce this behaviour to 1=(L 2 log l L). We show that the nite-size-scaling and the perturbative limit do not commute in the calculation of the corrections to nite-size scaling. We present a detailed study of the corrections for the RP 1-model.