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 ϕ4 model with a one-component order parameter. Problems of previous perturbation approaches for T < Tc are discussed and an improved perturbation theory is employed that is applicable both above and below Tc. The susceptibility, order parameter, specific heat, and a cumulant ratio are calculated for fixed d < 4 in one-loop order for the case of a cube with periodic boundary conditions. Finite-size scaling functions are evaluated in three dimensions without using the ε = 4 − d expansion. Quantitative agreement with Monte-Carlo (MC) data of the three-dimensional Ising model is found in most cases. Additional MC data of larger systems would be desirable in order to test the detailed predictions of the finite-size field theory more conclusively in the asymptotic region.