Order-Parameter Distribution Function of Finite O\(n\) Symmetric Systems

We present analytic and numerical studies 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 ϕ⁴ field theory for a 3D cube with periodic boundary conditions by means of a new approach that appropriately deals with the Goldstone modes below T_c. Good agreement is found with new Monte Carlo data for the distribution function of the magnetization of the 3D XY \(n = 2\) and Heisenberg \(n = 3\) models.