We propose a new perturbation approach to finite-size effects near the
critical point within the phi 4 held theory for an n-component order
parameter with periodic boundary conditions. Our approach is applicabl
e both above and below T-c. Calculations of finite-size scaling functi
ons of the specific heat, susceptibility, order parameter, and a cumul
ant ratio are compared with Monte Carlo data for the three-dimensional
XY model. Good overall agreement with the Monte Carlo data is found.