Order-parameter distribution function of finite O(n) symmetric systems in an external field

We study the effect of an external field h on 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 Tc. The result describes 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 Tc. Theoretical predictions of the finite-size scaling function are presented for the Ising (n = 1) and XY (n = 2) models. Good agreement is found with recent Monte Carlo data for the distribution function of the magnetization of the 3D Ising model at finite h above and below Tc.