Corrections to finite-size scaling in two-dimensional O(N) sigma-models

We have considered the corrections to the finite-size-scaling functions for a general class of O(N) sigma-models with two-spin interactions in two dimensions for N = infinity. We have computed the leading corrections finding that they generically behave as (f(z)log L + g(z))/L(2) where z = m(L)L and m(L) is a mass scale; f(z) vanishes for Symanzik improved actions for which the inverse propagator behaves as q(2) + O(q(6)) for small q, but not for on-shell improved ones. We also discuss a model with four-spin interactions which shows a much more complicated behaviour.