Order-Parameter Distribution Function of FiniteO(n)Symmetric Systems

We present analytic and numerical studies of the order-parameter distribution function near the critical point of $O\left(n\right)$ symmetric three-dimensional (3D) systems in a finite geometry. The distribution function is calculated within the ${\varphi }^4$ 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 $\mathrm{XY}$ $(n=2\mathrm{})$ and Heisenberg $(n=3\mathrm{})$ models.