We compute the corrections to finite-size scaling for the N-vector model on the square lattice in the large-N limit. We find 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 behavior to ${1/(L}^2{\log }^{l}L).\mathrm{}$ We show that the finite-size scaling limit and the perturbative limit do not commute in the calculation of the corrections to finite-size scaling. We present a detailed study of the corrections for the ${\mathrm{RP}}^{\infty }$ model.

• Received 2 April 1998

DOI:https://doi.org/10.1103/PhysRevD.58.105007