Renormalization-group theory of critical phenomena in confined systems: Order-parameter distribution function

We present a renormalization-group study of the order-parameter distribution function near the critical point of O(n) symmetric three-dimensional (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 deals with the Goldstone modes below T-c. Results are given for both vanishing and finite external field h. The results describe finite-size effects near the critical point in the h-T-plane including the first-order transition at the coexistence line at h = 0 below T-c. Quantitative theoretical predictions of the finite-size scaling function are presented for the Ising (n = 1), XY (n = 2) and Heisenberg (n = 3) models. Good agreement is found with recent Monte Carlo data.