FIELD-THEORY OF FINITE-SIZE EFFECTS FOR SYSTEMS WITH A ONE-COMPONENT ORDER-PARAMETER

The field-theoretic renormalization-group approach is used to describe finite-size effects near the critical point of the phi(4) model with a one-component order parameter. Problems of previous perturbation app roaches for T < T-c are discussed and an improved perturbation theory is employed that is applicable both above and below T-c. The susceptib ility, order parameter, specific heat, and a cumulant ratio are calcul ated for fixed d < 4 in one-loop order for the case of a cube with per iodic boundary conditions. Finite-size scaling functions are evaluated in three dimensions without using the epsilon = 4 - d expansion. Quan titative agreement with Monte-Carlo (MC) data of the three-dimensional Ising model is found in most cases. Additional MC data of larger syst ems would be desirable in order to test the detailed predictions of th e finite-size field theory more conclusively in the asymptotic region.