Abstract
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 ϕ 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. 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 T c. 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 T c.
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