FIELD-THEORY OF FINITE-SIZE EFFECTS IN O(N) SYMMETRICAL SYSTEMS

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.