RENORMALIZATION-GROUP THEORY OF CRITICAL PHENOMENA IN CONFINED SYSTEMS - ORDER-PARAMETER DISTRIBUTION FUNCTION

We present a renormalization-group study of the order-parameter distri bution function near the critical point of O(n) symmetric three-dimens ional (3D) systems in a finite geometry. The distribution function is calculated within the psi(4) field theory for a 3D cube with periodic boundary conditions by means of a novel approach that appropriately de als with the Goldstone modes below T-c. Results are given for both van ishing and finite external field h. The results describe finite-size e ffects near the critical point in the h-T-plane including the first-or der transition at the coexistence line at h = 0 below T-c. Quantitativ e theoretical predictions of the finite-size scaling function are pres ented for the Ising (n = 1), XY (n = 2) and Heisenberg (n = 3) models. Good agreement is found with recent Monte Carlo data.